My view: if it's magic, you don't die otherwise you do. Unfortunately I've nothing more to say on the matter. :P

How DOES a healing potion work ?
In my opinion it disappears almost immediately upon contact with the first living organism it touches (so it can be applied to skin), launches (passing through solid matter) into the nearest damaged body-sector and restores it into its default, healthy "backup" state. It's not water, it exists in a quasi-material state only temporarily. If you drop a mutilated (but not FUBAR) person into a healing potion pool - they soak up everything they need... and stop after being healed to 100%. Any damage (including functional like loss of consciousness, lack of oxygen where necessary) should get healed up to the point of 100%, at which point the healing would stop... If the potion itself was causing the damage (as in the drowning scenario), I imagine it would ease any and all pain, prevent organ damage and very slowly disappear from the pool until the person stopped inhaling it (by emerging from it or it simply disappearing at some point).
Everything is, of course, dependent on specific mechanics present in the world we're discussing. The above is merely how I would look at things. It's not syrup, it's a magical backup restoring procedure.

Call me a sexist macho but I gladly tell you this is a very female approach to the problem!

Back on topic:

Mathematically speaking:

Having a health potion with regenerative effects like X Hitpoints/second will be successful in keeping someone drowning alive as long as the drowning damages the body suffers from is less than X Hitpoints/second. If the "drowning damage" is higher than the healing generation: Bam! You're dead, otherwise you get a little better every second (not very effective, just like having a bad roll) until the potion dissolves completely into your thorax/lung/bronchia something. Doesn't really evokes pleasant feelings, methinks.

Okay...

Having an "instant" health potion that would dissolve instantly while emitting its healing power would counter the drowning effect completely and thus would counter the killing effect of choking you. (depending on the power of the potion)

It's like getting hit by an Icebolt while drinking a potion, both effects are negated but you survive.

If the health potion emits its healing power immediately while not dissolving completely in the same instant you get healed to full health but drowned afterwards by the remaining liquid which lost its healing properties.

If the healing liquid evaporizes quickly or even features some sublimation features things might be even more complicated.

But now to something completely different:
Mana potions replenish mental energy. Considering how much a headache that mental business (like thinking or acting sapient) causes to everybody it defintely has to taste like ass.

What games feature limb damage or loss?
I think Fallout does it, and there normal stimpacks won't fix your limb damage unless you apply them directly to the broken limbs while sacrificing the hit point boost.
In hardcore mode I think you might have to use doctor's bag or other curing methods to restore limb condition while hit points (health) are a different matter.

If you want a fantasy setting try Dragon Age, where characters have to heal crippling conditions at the camp while healing spells/salves/potions only work for hit point restoration.

If you want to get very philosophical, or better yet, technical, the answer is no.

Reason:

The question asked is: Let's start by defining health potion.

A health potion would be a liquid in a container. The liquid heals your wounds. Important part here is container. Health potions are always in containers, so it´s not like you are swimming in a pool of health restoring liquid.

Of course, now you will say something like: You can drown drinking water.

Well, water is not guarantee to restore your health for any amount. Unlike health potions that have the right amount of liquid in the container to guarantee to restore the amount of health it restores, granted you are wounded enough to gain that amount of health.

Then again, if you try to drink the potion including the container, of course you can suffocate, but that would be suffocate, not drown.

PS: I think everyone in this post (including myself) have been playing too many games.

Some of us still play those dorky tabletop games with the dice. :p Limb loss can be a relatively common occurrence in those, depending on your GM's style.

"Choked on a health potion" sounds like a sardonic gravestone epithet that would be found in Arcanum or Baldur's Gate.

This question is about is meaningful as musing about the nature of "health kits" instantly repairing any sort of horrific wound you have simply by running over 'em. They must be G.E.C.K. health kits, natch.

Because while it can restore damaged tissue and restore and organ's functionality, it can't supply your lungs with oxygen.

This. Yay, now I don't have to type it!! :-)

Depends on the potion ;-) While still experimental there are good chances you can breath liquid. If the potions are oxygen-rich (why not, oxygen is known as a good stimulant) it's reasonable you can breath them.

I played Angband or Moria a long time ago and had a gravestone epithet for one of my later characters named Elvis:
"Rest in peace Elvis, death by lots of overeating" or something. While pondering this very question this amusing event came to my mind again.

I think it depends on the exact nature of the healing potion, but normally a healing potion doesn't heal brain damage, and I think it's not assumed that it will oxygenate your blood, so if you are under water then even if you drink it while submerged you will die due to lack of oxygen. Your body will be perfectly healed of any physical damage but your brain will shut down.

Nah. Health potions only restore HP = physical damage (and depending on the game - status ailments).

Drowning to death is not something that any Health Potion could prevent. ;)

Besides how many Health Potions are we talking about? Enough to fill Hammer Space? LOL

I think some of you are making the mistake of taking to much real world info into this account.
There are very few "Brain Damage" bars in RPGs, we have a health bar.
If something is damaging to you, your health bar drops and you can use health potion to counter that effect.
If you have status effects (depending on the RPG Ruleset you want to apply) things get more interesting, but don't cramp in "brain damage" when the game world doesn't have that type of damage.

Considering that you can "apply" a giant club a million times to the forehead and heal the damage with health potion, the residual remaining brain damage either does not exist or is healed as well...

You people are focusing too much on the potions ("depends the game's healing mechanism, what kind of potion", etc).

It's a matter of drowning mechanism. Some games make drowning an insta-kill, like being crushed by a rock. Some make of drowing a slow, or a very fast, total healthdrain (actually some games do it with crushing rocks too).

If drowning is not boolean, then potions could keep you alive as they drown you. But if it's death-toggle, potions would just kill you.

It depends on how DROWNING works, not how the potion works.

I mean, duh.