Things can get complicated where gun laws are concerned but in general terms it's legal to suppress an airgun. It can get more complicated in some areas but in the US (and again in general terms) if the suppressor is permanently affixed to the barrel then Federal law permits it. The usual caveat is to check your local laws no matter what we're discussing.

Air guns can be excellent tools, and some do indeed have enough power to harvest large game. It's hard to say which would be a better 'survival' tool since that depends on a lot of things. An air rifle doesn't need ammunition in the way that a firearm does but they do require pellets, you can't use a rock or something. So you still need to stock ammo of a sort. In general terms a firearm doesn't require much in the way maintenance beyond routine cleaning and occasional replacement of some of the springs [usually over a period of years].

Probably long terms survival will require hunting to be supplemented with trapping and/or fishing. Again, it really depends on the situation. Most experts hold that food is a pretty low priority in the most common situations. Of course we have read about some of the "Black Swan" situations where folks have survived two months before being rescued. The environment where you will be operating will dictate what you should have with you.

To be clear I'm not discussing an EOTWAWKI situation. It's hard to imagine how one could adequately prepare for the total collapse of human civilization, and I'm not sure I would care to survive it to begin with. In any event it's beyond the normal scope of ETS I suppose.