It's possible, I'm not sure about the black tips on those claws for your particular one. My experience with the plain brown, hairy ones is that they leave everything alone but are opportunistic scavengers. If they get the chance, they will grab a fish, but usually the fish has to be sick or injured.
If you are losing fish, I would do a precautionary large water change before looking at the crab - that's how infrequently they tend to take fish IME.