I can tell you a lot of Garand shooters at the CMP forum claim good accuracy from 110 and 125 grain bullets in reduced range matches, so I don't see a reason, accuracy-wise, that it couldn't be made to shoot well in the 300 BLK. As to effect on game, it will depend on impact velocity.
Varmint bullets are intended to open very quickly and be maximally distructive (explosive) on varmints in their design impact velocity range, so they may be expected to be too distructive of meat if you try to hunt small game with them and to fail to penetrate medium game well. But that assumes your are in their design impact velocity range. If you stay on the low end or below that range, you may get minimal expansion, though if you are trying to limit expansion to spare meat, a 110-grain RN FMJ would be a lot less likely to totally destroy small game.