I don’t know much about air guns, but depending on the power of an air gun, it could procure some food for you.

However… would it not be more prudent to get a real gun for that? Rifles and pistols chambered in .22 LR have many of the same benefits of air guns: ammunition’s cheap, ammunition’s small, and relatively quiet. Additionally, a .22 LR will have a much greater range, better accuracy, a pretty good assurance of making a clean kill on small game, and even has a chance against larger (maybe even two-legged if you aim well) game.

I cannot speak for you, but if I were in an “emergency situation”, I would want something that is extremely reliable, has an excellent chance of doing its intended job, and is versatile enough to do other jobs as well. An air gun could work if it’s all you have, but I would look into getting something better suited to the task. Emergency situations are not a time for guesswork.