Not an M1 Garand, because that's for regular army. Some aircraft had a Thompson on board, but you would never bail out with it. Instead, you would ditch and retrieve it from stowage. Fighters would not have one on board, but aircraft like the B,26 B-24, C-47, TBM, and SBD would. I don't know about the B-17. but maybe the B-29 although it would seem unlikely that you could survive ditching a B-29.
Right now though there doesn't seem to be much for a downed pilot to try to shoot, except troops.