I don't know what an avatar is....
but I wouldn't mind a small (1" x 1" maybe) picture that would be displayed under the username. That way it wouldn't take up any extra space and there would be a size cap (and a limit of one picture)
Another message board I occasionally frequent does that and it's not a problem at all.
I can see allowing pix in signatures getting out of hand with size and stuff, but a small picture on the side is fine -- sort of like a buddy icon pic from AIM