I say it would hurt, but that's just my opinion. Does a tailbiting betta feel the pain of biting ones self? Maybe. Does a bird feel the pain when it plucks it's own feathers out? Yes. But there is a reason for these behaviors, with birds it is often stress, bordom and/or neglect, with fish, I think they get bored too, it could also be stress from water conditions or parasitic infestation.
My goldfish was trying to scrape his gills on his gravel, apparently he had gotten parasites of some sort, who's to say that biting a tail is not a bettas way of saying something is wrong.
Okay, I lost my point somewhere in here and I am too tired to figure it out, so, good luck finding it.