As long as he's eating, its difficult to watch him not be active but that would be the most encouragement that he'll make a recovery. I don't have alot of experience with hawkfish but they seem like kind of lazy fish, perching here or there and if there is a lot of flow they rely on their pectoral fins to balance them (much like blennies which I do have experience with, they're lazy buggers).
If he does have an issue with his tail, it may totally not be noticeable, there could be some nerve damage or a bit of damage to the bones leading up to it if he got it caught in something or whacked it against something. That will likely heal as well, just takes time. You'll just have to be patient and we'll hope for the best
