For what it's worth...
And I've seen small game taken cleanly with a blank round chambered behind a twig shoved into the barrel.. not a great idea, but it works at close range.
I have a fair bit of North American big game experience - all critters but one with something a lot more appropriate than a 22 rimfire.
The 22 long rifle is a very lethal round - but not neccessarily incapacitating. Relatively deep penetration and a long skinny permanent wound channel, no matter what kind of ammo you feed it (forget exploding water-filled cans - it ain't the same thing). Very very lethal for the patient person who places shots precisely.
Statute of limitations having expired long time ago - it will in fact cleanly take a whitetail IFF the shot is precise. One shot, one pile of meat. First deer - amazed me. A .458 wouldn't have dropped it any quicker. The only deer I ever had step out of its tracks was a heart-lung-shot with a very heavily constructed 30 caliber 180gr bullet (elk was the venue, but there was a deer tag as well) - the wound channel was amazingly like a 22, only bigger. Same bullet I've hammered griz and moose with. Bambi run, bambi fall <shrug> would have had the same result, more or less, with a 22. Maybe a little longer run - or not.
And 22 rimfire is very quiet in a rifle with subsonic velocity ammunition. And the ammo is small and not especially heavy, as ammo goes.
But - exactly what sort of "survival" situation are we talking about? I would not choose the 22 on purpose unless I was intending to stay a long time or travel a long distance and hunting meat for the pot was part of my plan.
The ammo is not particularly waterproof compared to factory centerfire ammunition. It appears to have a shorter "shelf life" (not that it would matter in anything other than a TEOTWAWKI situation). And... there's that "precise" and "not neccessarily incapacitating" caveat. Not what I would prefer to face a large canivore or POed moose (elk to Europeans) with.
I have a choice of firearms to take into the wilds with me and on some trips for specific reasons, a 22 has been the caliber of choice for me. But not usually. On extended duration trips on foot where fresh meat was hoped for, I carefully loaded "small game" rounds for my centerfire rifle of choice for that trip. Noisy compared to 22? Sure. Large compared to 22? Sure. But it does the job. Some folks carry a sub-caliber device and sub-caliber ammo for the same purpose, but I've never been enamored of that approach. Simpler to depress the top cartridge in the magazine and slip in a tailor-loaded cast bullet cartridge that I had complete control over for velocity, accuracy, etc.
Oh - one can take fish with a 22 as well - but I decline to elaborate - it does not involve shooting in the conventional sense and for goodness sake, don't shoot a 22 over water - can we say "skipping stone"?
I'd consider a 22 an expert's caliber for harvesting meat, not a first choice for most of us (myself included).
My 2 cents worth.
Tom