Does the Elixir of Life heal injuries?

Question

We know that in the Harry Potter series the Philosopher's Stone can produce the Elixir of Life, which grants dramatically increased longevity. The only known maker, Nicolas Flamel, lived for over 600 years.

But we also know that the Elixir of Life is capable of more than merely arresting aging, since Voldemort would have used it to return himself to a physical form.

Of course he was prepared to drink it if it would take him out of the horrible part-life to which he was condemned after attacking you, but only to regain a body.

—Harry Potter and the Half-Blood Prince

So in the spirit of this question, which asks whether Horcruxes are proof against old age, I ask the opposite question.

Does the Elixir of life protect one from lethal physical injury?

Answer 1

I haven't been able to find any canon confirmation, but my guess would be NO.

All we know from the books is that the Elixir of Life is enough to "make the drinker immortal":

The ancient study of alchemy is concerned with making the Philosopher’s Stone, a legendary substance with astonishing powers. The Stone will transform any metal into pure gold. It also produces the Elixir of Life, which will make the drinker immortal.

There have been many reports of the Philosopher’s Stone over the centuries, but the only Stone currently in existence belongs to Mr Nicolas Flamel, the noted alchemist and opera-lover. Mr Flamel, who celebrated his six hundred and sixty-fifth birthday last year, enjoys a quiet life in Devon with his wife, Perenelle (six hundred and fifty-eight).

_{-- HP and the Philosopher's Stone (text available on Pottermore)}

Exactly how this immortality is achieved is never made clear; it could be:

• by making the drinker younger again or arresting their ageing, so that their lifespan is extended
• by somehow preventing any disease or injury from overcoming them, so that they cannot die

The first of these would not protect against injuries, but the second would. I strongly believe that the way the Elixir works is more similar to the first, for a couple of reasons.

1. Cheating Death itself becomes a major theme in the final book, HP and the Deathly Hallows. The Hallows were all created in an attempt to avoid or cheat Death, and none of them is completely successful in doing so. The most successful was the Invisibility Cloak, the one that doesn't involve taking on Death directly but only hiding away from it until the time is right.

   If the Elixir of Life was a way of warding off all possible death-causing injuries, it would violate the philosophy that JKR has set out in her books. You don't cheat Death; you simply avoid it until the time comes for you to meet it peacefully and on your own terms. Preventing a person from dying altogether would be far too powerful an effect; merely preventing them from ageing, and leaving them susceptible to other kinds of death such as disease or injury, seems much more in line with the Potterverse philosophy of death.

2. JKR didn't invent the idea of a Philosopher's Stone or an Elixir of Life; both are very old concepts in the ancient art of alchemy. On these traditional mythical objects, there is far more information to be had than on the fictional objects created by a single 20th-21st century author. And this information will be relevant, because JKR says both have the same properties:

   I did not invent the concept of the Philosopher's Stone, which is a legendary substance that was once believed to be real, and the true goal of alchemy.

   The properties of 'my' Philosopher's Stone conform to most of the attributes the ancients ascribed to it. The Stone was believed to turn base metals into gold, and also to produce the Elixir of Life, which could make you immortal. 'Genuine' alchemists - the forerunners of chemists and physicists - such as Sir Isaac Newton and (the real) Nicolas Flamel, sought, sometimes over lifetimes, to discover the secret of its creation.

   The ideas of the Elixir of Life and the Philosopher's Stone are thousands of years old, and most (though admittedly not all) references to them are in terms of renewing the drinker's youth, not protecting them from sickness or injury. From the Wikipedia links above:

   The elixir of life, also known as elixir of immortality and sometimes equated with the philosopher's stone, is a mythical potion that, when drunk from a certain cup at a certain time, supposedly grants the drinker eternal life and/or eternal youth.

   
   

   It is also able to extend one's life and called the elixir of life, useful for rejuvenation and for achieving immortality; for many centuries, it was the most sought-after goal in alchemy. [...] The most commonly mentioned properties are the ability to transmute base metals into gold or silver, and the ability to heal all forms of illness and prolong the life of any person who consumes a small part of the philosopher's stone.

   Sometimes it's referred to as being able to heal injuries and disease, but this can be put down to the natural exaggeration and embellishment over time of any magical object's properties. It's more commonly referred to as simply providing the drinker with youth or prolonging their natural lifespan. When JKR says her Philosopher's Stone conforms to "most of the attributes" of the ancient mythical object, perhaps this is what she means: it has the power to prevent a person from dying of old age, but not to prevent them from dying altogether.

Answer 2

My best guess would be no. The best information about how the Elixir of life works seems to come from Dumbledore:

    "As for the Stone, it has been destroyed."
    "Destroyed?" said Harry blankly. "But your friend - Nicolas Flamel -"
    "Oh, you know about Nicolas?" said Dumbledore, sounding quite delighted. "You did do the thing properly, didn't you? Well, Nicolas and I have had a little chat and agreed it's all for the best."
    "But that means he and his wife will die, won't they?"
    "They have enough Elixir stored to set their affairs in order and then, yes, they will die." _{Philosopher's Stone, Chapter 17, The Man With Two Faces}

From this I'd surmise that the Elixir is time-sensitive. It seems to work like Felix Felicis or the Polyjuice Potion; its effects will last for so long and then eventually wear off. To benefit from immortality one has to produce Elixir through the Stone and take it at regular intervals. If you stop taking the Elixer then presumably your body will rapidly re-age. When you suddenly go from having the body of a 30 year-old to a body of (say) a 430 year-old you'd become so frail and weak that you would most likely die straight away. This seems to be what happened to the Flamels when they stopped taking the Elixir. The Elixir of Life has to be continually administered to be effective.

There is no canon information that I'm aware of that settles the question of whether the Elixir would heal you of injuries. It may work like phoenix tears, it may not. However, based on my previous paragraph, I'd suggest that if the Elixir-taker were stunned, immobilised or had the Philosopher's Stone taken away that eventually the Elixir would wear off and they would succumb to a natural death from old age. So, no, you can't throw yourself off a cliff and expect the Elixir to break your fall. The Elixir makes you immortal, not invulnerable. Similarly, if you were hit with Avada Kedavra I don't see any reason why the Elixir would protect you from a spell that has no come-back.

In short, there's no indication that the Elixir of Life has any protective qualities whatsoever.