No - not in a worthwhile way.

Given the current state of medicine, organ break down is not your main problem any more. Operations to replace organs with artificial ones work, although there is still a non-negligible risk to it. Even if we assume that we can replace major organs affected by cancer and ignore the spread of cancer through metastases, there are more drastic limiting effects of irreplaceable body parts.

Three parts of our body form the main problem, responsibles for ~75% of deaths in elderly people:

• 
  blood vessels: they run everywhere in the body from wide vessels as the carotis to extremely narrow capillaries in the brain. They age naturally and there is no way of replacing the smaller ones in less accessible body parts such as the brain. If they get clotted or burst, your suffer from thrombosis resulting in stroke, heart attack or other cardio-vascular symptoms.


• 
  nervous system: nerves are hard to replace, they actually die off, making elderly people lose capacities such as sensitive touch, hearing, temperature feeling and regulation etc.


• 
  brain: the main problem limiting life span or better to be said the life span lived with a certain quality of life is the brain's capacity. Altzheimer's disease, dementia, the natural deterioration of reflexes and mental constitution are all effects limiting the human life span automatically and most radically. Unless you can keep these mental effects in check, no organ replacement will make people life longer in a worhtwhile way of living.
  

That depends on your definition of "life"... But the answer is probably no.

If you replace the heart of a healthy human with an artificial one, that human won't die from a heart failure. But he can still die from cancer, stroke or a broken neck because he fell down the stairs. That means the overall number of deaths due to physical cause will be smaller, but not zero.

The human body is already able to stay relatively healthy into old age if it's maintained and moderately trained. The same applies to our brains. As long as people have something to do in their life, most stay clear minded into old age. But if they lose that purpose or task, the brain power decreases just as much as an unused muscle.

By replacing vital organs you can keep the body alive and minimize the numbers of deaths due to organ failure and unhealthy lifestyle. But those people might be no more than human vegetable if they don't have any reason to keep their brains active and trained to manage the basics of life.

The more sophisticated a society is, the more likely it is that people lose their mental prowess. Our great-grandfathers (and mothers) had to learn many things about agriculture, observe nature and contribute to the family even in old age. Their bodies degenerated faster than their brains.

In our current society, we learn a lot of stuff in school (most of which we never use in life), but we have computers, smart phones, calculators and navigation systems to do the hard thinking for us. After retirement many people lose any purpose in their life and their brains degenerate rapidly due to the lack of mental training. (This effect is called Digital Dementia)

If this trend continues in the future, the degeneration of brains might set in even earlier in life and be more devastating, because all the gadgets that make life so comfortable mean people never need to train their brains.

What you consider to be important becomes dependent on what can fail without replacement. So ultimately your answer is the more specific problem of Theseus' Ship.

• Once you have replaced the entire body (apart from the brain) with artificial replacements, are you still alive?


• If you also replace the brain with an artificial unit are you still alive?


• If you only replace the brain with an artificial replacement that to all other parties appears to be you, are you still alive?

If the answer to all those questions is yes, then yes, replacing all important parts with artificial replacements will lead to longer life.

TLDR: No, as transplanting an organ have drawbacks. Replacing a functional organ is just asking for trouble

Transplant can fail:

Everyone talks about the success rates of kidney transplants. Rarely
do we talk about what happens when transplants fail. People will quote
the official statistics that 97% of kidney transplants are working at
the end of a month; 93% are working at the end of a year; and 83% are
working at the end of 3 years
https://www.kidney.org/transplantation/transaction/TC/summer09/TCsm09_TransplantFails

Those are just some numbers about current succes rate of kidney transplant. 83% of succes rate is very good for thos who would die without transplant. But they are just disastrous if the people were healthy.

Complications

A transplant can have lot of complications. Just for a heart tranplant, you can get:

• Organ Rejection


• Infections


• Graft Coronary Artery Disease


• High Blood Pressure/Hypertension


• Diabetes

No long term support

here is an abstract about long-term outcome following heart transplantation. It's not dramatic in current world, as people with heart problem are in the majority of cases quite old. But it's problematic for transplantation on younger folks

Money cost

Another problem is the cost of a transplantation. A surgery operation cost a lot. An artificial organ even more. Replacing every organ of every human would be just way beyond budget accorded to health organization. ANd this money could be spent way better on other fields. Organ failure is just one way to die. They are plenty others way to die, either enverinomental (accidents for example), or other diseases (cancer, ischemic stroke, diabetes...)

That would be a more or less definite "No" for both questions.

There is leeway for a "yes" concerning some individuals. Obviously, when your kidneys (or your heart) are failing, your life expectancy with artificial kidneys (heart) is much better than without.

For average life expectancy, it's a different story, and for absolute life expectancy, yet another.

Surgical interventions (even narcosis without surgery) are a possibly lethal risk, so the extension of average life expectancy is limited by that factor. Replacing several organs is not just "some surgery" but a really awful darn lot of high-risk surgery. Thus, the risk (and impact on life expectancy) is relatively high. On the other hand, organs as-delivered by nature work amazingly well for an amazingly long time in most cases, which is pretty close to the total maximum. So the possible gains are not great. In summary, this will likely rather decrease than increase the average.

Now, there exist ideas which are repeatedly being spread by uninformed and stupid people such as "life expectancy rises X years every 5 years, soon we will live 150 years" or "in 10-20 years we will be able to cure cancer" (the German Health Minister made that claim a few weeks ago). They're just that, ideas, and uninformed.

The oldest-ever-person lived 122 years, she died 22 years ago. The next oldest lived 119 years and died 24 years ago. Recent deaths (2017-2018) of long-lived people were in the 116-117 year ballpark. If the idea of us being able to raise life expectancy by magic or medicine was true, we should have seen someone beating the 122 year record during the last quarter-century. That didn't happen.

Also, consider that the penny dreadful of people generally living shorter lives in the old days is simply untrue. What's true is that if someone chopped off your head or thrust a spear in your side, or if you died from plague or dysenteria, then truly your life expectancy wasn't so awesome. However, if you were left alone to live a peaceful life, you could very well get old a thousand or two thousand years ago. No problem.

Socrates was murdered tried and executed at the age of 71, in perfect health. Ramesses II lived, if archeologists translated correctly, 90 years. That was 3400 years ago.

There's a good chance you die at or after birth (or while delivering), medicine can help with that. That's why the average has gone up so drastically, too. Obviously, if half of the population doesn't die during the first few years, then the average lifespan gets longer. But in reality, this doesn't mean anything.

There's a chance you die from a variety of diseases, medicine can sometimes help with that. Alright.

If you get through that unharmed, you'll live 100-120 years, and that's the end, do what you will.

There's strong indicators besides the verifiable fact that nobody actually manages to get older (despite there being no urgent reason to die).

For example, the delicate balance between proto-oncogenes and tumor-suppresors. Which, if you think about it, makes the "we will be able to cure cancer" statement a really funny joke (funny because its naivety). Nature doesn't work as simple as "press button here". Yes, we can do kinda awesome things that nobody could imagine 30 years ago. But whatever it is, it's still just a crude hammer, and Nature is a fine clockwork (and we don't fully understand the construction drawing).

Our entire life is about wandering on a narrow ledge, and the abyss is both to the left and to the right. Go too far to the right and your cells just die (this has been demonstrated in vivo using p53 on mice). Go too far to the left, and you get an entirely different problem (kinda obvious).

There's that other magic cure for everything called stem cells. Except they're no cure for everything either. There's a limit to how often you can make them reproduce, and there's a limit to how fault-tolerant their DNA is over a century. Oh right, there's CRISPR/Cas9 to solve all our problems. Please. Don't.

No, sorry. No magical life extension any time soon. That's just not realistic, even less so from something as crude as replacing a few organs.

If nothing else, your senescent brain cells will eventually just die, and there you go, goodbye.

You mentioned in a comment that you meant current technology, so, definitely no.

We just don't have the organs yet.

Artificial hearts exist. They can work for years without a hiccup, but they can also fail catastrophically at any moment. Many do. I admittedly didn't do any research, but I'm very confident that their failure rate is much worse than that of the average natural heart. Charging is also an issue.

The closest we have to artificial kidneys are those huge dialysis machines which obviously could not be implanted in an elephant, much less in a person.

To my knowledge, there's no current technology able to replace lungs, liver or intestines, except transplanting a natural one, which has obvious scale limitations.

Assuming the artificial organs work just as well as current one's but eliminate the organ's failure, a definite yes. It wont expand it indefinitely though.

• With this much organs being replaced you reduce the amount of potential cancers.




• Any cancers that do develop are less likely capable of destroying the artificial organs by growing through it (which is why cancer is so dangerous, it causes organ failure. Just having cancer will not kill you). And if they are capable the cancer needs more time to kill off the organ.

This leaves basically two things to kill you: deterioration of the brain, which often takes longer than most causes of death so you already have a longer lifespan, and deterioration of your bloodvessles and supply which eventually causes the artificial organs and brain to die off. Potentially also failure of your immune system depending on if it's artificial or not. Regardless, the average lifespan definitely increases!

Some statistics can be found here: https://www.who.int/news-room/fact-sheets/detail/the-top-10-causes-of-death

Interesting here is that you actually see the exact effects of your proposal reflected in the changes in death causes. As medicine advances and things that would cause death before become cureable, allowing people to live long enough to die of something else. This allows cancer, alzheimers and other diseases to get more deathcauses. Its almost perfectly with your scenario except the medical care doesnt come from artificial organs.

Yes, to some extent.

The benefit of replacing organs with artificial ones is that humans become like cars, and medicine becomes like car repair. When something breaks, you find the broken part and replace it. Currently, people die from organ failure. That wouldn't happen. Liver cirrhosis: wouldn't happen. Early-stage pancreatic cancer: wouldn't happen. Type 1 diabetes, most heart conditions, ruptured organs, emphysema, arthritis and blindness would all be curable if we had the option to replace damaged or defective organs. You could replace entire bones at a time to reduce the effects of osteoporosis.

However, it wouldn't make us immune to everything. I'm drawing the line here at the brain, since replacing the brain but preserving your consciousness and memories is far beyond the technology we're discussing here. 10 percent of Americans over 65 are afflicted with Alzheimer's disease, which affects the brain. Alzheimer's is the 6th leading cause of death in the US. It wouldn't be solved at all by this new form of medicine.

There's also the matter of cellular senescence. When cells divide, small amounts of their DNA are lost. This results in the cellular DNA shortening slightly with every division. To protect against adverse effects from this, the ends of your chromosomes are tipped with sections of random DNA called telomeres. This provides a buffer of DNA that can be safely deleted without damaging your genes. However, as you age, the telomere shortens, and eventually, the functional DNA in your cells is damaged, causing the cell to stop working and just sit around doing nothing, taking up energy. The more of these 'senescent' cells you have, the less efficient your body is, and the more likely you are to develop chronic problems. Replacing individual organs would only help with this to some extent, since we are more than just a collection of parts: every cell has its own complexities.

Of course, metastatic cancer would be completely unaffected by this treatment.

So while organ replacement would make several life-threatening ailments trivial matters, it wouldn't address other, equally deadly problems. Statistically, this would increase life expectancy by a decade or two, maybe, but it wouldn't halt aging or remove the medical problems associated with it.

TL;DR
Life Span will Increase.

How much is a statistical calculation someone could do, but a other quest to your question:

How many parts of the human will be replaced with artificial parts and the "Person" will be still called human?

If everything is Replaced but the Brain, couldn't you just put the Brain into a Vessel for it. So just removing the Brain from the Body.

One thing you still have, and it would be the deadliest killer is Brain Cancer.
Other things would be more like Accidents or murder.

And then: why do so many people die before there "best by date"?
If you have the technology to replace body parts with artificial ones (that are working without problems) then you have also the technology to repair the damage sickness could do OR replace it when its not possible. And even today body parts are replaces by artificial and ones from other Humans. They are expanding the lifetime of that human (from hours/day/months to years/.. most of the time) so why shouldn't it be if the entire body could be replaced.

Of course, but not much

I don't have any place to quote it, but, it's very common that the common reasons for dying of old age are basically acumulative damage done in any part of your body due to its usage.

Some examples are:

• 
  Cancer. Each cell division slightly increases the risk of cancer due to telomeres shrinking, replacing an organ (and its cells) will "reset" the chancer factor due to age in that specific organ.
  
  

  
  

  Common environmental factors that contribute to cancer death include tobacco (25–30%), diet and obesity (30–35%), infections (15–20%), radiation (both ionizing and non-ionizing, up to 10%), stress, lack of physical activity and pollution

  
  

  
  


• Cardiac diseases, a heart is like a machine, it gets rusty over time. A heart in any animals has between 1 to 1.5 billions of beats in a whole lifetime. Just check in Google, like here. Humans are the only race who can have a bit more than 2 billion due to medicine. After that usage (i.e: when you age), statistically speaking you are dead, the chances of dying for a cardiac arrest are very high. Imagine if you could replace it after reaching the limit like you replace an old car with too many miles/kilometers.


• Well, basically any disease related to old age.

Replacing dysfunctional/old organ will obviously increase the lifespan due to a decrease in death risk for those diseases.

Sadly, there are three problems:

• 
  Philosophical: Did you know what is the Ship of Tesseus? Is a philosophical paradox, basically is, if you replace all your body parts when you stop being "you"?. Lucky, you don't replace your brain, no problem.


• 
  Orgain Rejection: With our current technological level, is very difficult to replace an organ, and there is always a chance of failure or refusal from our body.


• 
  Brain Damages: You said we can't replace our brains, that means that one part of our body (curiously one with the worst self-healing properties) can't be replaced and will always accumulate damage. At some point, it will stop working... and so we would die.

That is why I can say it will increase our lifespan, but not much. Our brain is very close to the limit. Have you heard for example about alzheimer? It's is a mental disease caused by the brain due to old age, one every 17 people of +65 years has it, and it can be deadly. If a cardiac arrest didn't kill us before (due to replacement) a brain disease will do it not much after.

Considering the comment by the OP, the question is:

Would replacing healthy organs with replacement organs be beneficial, using current technology.

If you're looking for a science based answer, the answer is unequivocally no. No current mechanical organ replacement gives as much of survival benefit as an allotransplant (organ transplant from another human). These devices are at best a bridge to transplant in patients who are healthy enough to get a new human organ. Additionally, allotransplant is unequivocally worse than keeping your own healthy organ. It is even worse than keeping a not particularly healthy, but not quite yet failing organ. As a rule, we try to manage unhealthy organs medically for as long as possible before even considering transplant. The major problems here are rejection and vascular events, or the problems that result from treatment of those problems, bleeding and infection. Organ failure (of the transplanted organ) is an issue as well. A new organ can feel like a new lease on life to someone who, for example, has been in stage IV heart failure, but it comes with major challenges. To use the metaphor a few other answers have used, OEM parts are best (human organs), but a replacement part of any kind is not an upgrade unless the original part has failed.

You can read about this in Schwartz's Principles of Surgery, Chapter 11, if you'd like to learn more.