Yup, puffs do eat snails, they love them hehehehe, they just love them to death!
As far as eating the crabs, Im sure they would like to if they could. But my crabs are too big for them to eat, and the puffs are so well fed that theyre really not all that interested in the crabs when they can have a nice jumbo raw shrimp or some scallops for dinner. Keep in mind I say "well fed" not "overfed". The ceylon puffer which is the largest at about 2 1/2 to 3" in size does occasionally try to nip at the anemone crab, but the anemone keeps him in check, he doesnt seem to interested in the emerald (the emerald is often just hidden away somewhere) or the other hermits in the tank, but the Ceylon is going to a friend in a couple days anyway.
It's actually quite interesting to watch when the smaller green puffs get too near the emerald crab, the crab holds up his arms like a prizefighter thats just won a boxing match and shakes them at the little puffs who back away.
I would imagine when these things reach full matrurity, then they would eat the size crabs in my tank, but the puffs wont be in my tank at that point since they will be too big, and have to be returned to the LFS.
But thats months if not a couple years away for these little green spotted puffs.
