I've been thinking about that a lot myself. I've had a .177 air rifle since I was a kid and it's a very simple to use, dependable system. My first air gun was actually second hand and pretty old when I got it. Aside from replacing the gasket a couple of times over the years it's still in perfectly good shape.
A decent airgun would definitely be an asset in skilled hands. It's way more accurate than a slingshot or thrown rock. Really, the accuracy is downright amazing at short range. I bought a Czech air rifle for under $100 and from a fixed position it will shoot a 3/8" group at 10y any day even with cheap ammo. This is more than good enough for taking headshots on small game with .177.
The main problem as I see it however is the lack of power (and short range). .177 would be just enough to take a small bird, mouse or squirrel at 10 yards at most (might be necessary to put a scope on the gun to ensure a clean hit). Maybe a very powerful .177 could take a rabbit with a headshot but I'm not sure. I've never shot a .22 air gun so I can't tell the difference. But all in all, these guns are seriously underpowered and at the same time bulky enough to be pretty cumbersome on the move.
It's a real shame there's no reasonably compact, large caliber air gun on the market (multi pump might be ideal on the trail) at an accessible price. Maybe something along the lines of the old Girandoni (repeating rifle w/ 20 shot capacity, about as powerful as .38 Special).
http://www.beemans.net/Austrian%20airguns.htm