I do not think you can create animated signature but you can create animated avatar. Animated avatars are annoying and the more you see more people using it the more annoying the avatars become. Animated signature will be worst.
Animated signatures would be a nightmare. I mean so many people will even consider to quit the forum than see them. It will be as annoying as advert pop up on random websites.
It will be a very big distraction from reading and engaging in the forum. Just imagine reading a post and brainstorming on how to respond and some silly write up will slide from right to left, or zooming from now where. Oh no, that would be horrible.