Oh yes, he most certainly can. Its very easily for a longer-finned male to turn around and take some good chunks out of their own tail, and its very common in males with big heavy fins like Halfmoons and Doubletails(which your guy is). The big longs fins are actually not natural, they're a selectively bred trait created in captivity for looks and showing purposes.....and some fish with bigger tails just REALLY don't like the weight, so they 'trim' their own tails. This can be anything from a couple of small nips once or twice, to bad chronic biting.
If he was like that when you got him its likely that he took some chunks out of his tail in the pet store cup, which is not at all uncommon since its such a small space. Its nothing really to be overly concerned about, just keep an eye on it and make sure his water is nice and warm and clean. If he doesn't continue to bite, you should start to see some clear re-growth soon. :)