Not normally. Think of it like a dog. Your fish and your dog don't have hands. They investigate with their mouths. Is it possible your tang is trying to eat your hermit? Sure, I guess, but it's unlikely. It's more like that it is just investigating the hermit which it will do by nipping at it.
Most of my fish will do the same thing to my snails if the snail falls off the glass and it's foot is out of the shell trying to turn over. They never come back a second time to eat it, but they all come sample it more as a way of finding out what it is and what's happening.