It can be done, seeing as other members have moving avatars (and I did at one time). Many dislike it because it can cause loading issues, but we don't disallow it.
As for the size, I'm not sure what our limit for moving avatars is. I know sites like Photobucket and Tinypic do have resizing options. You could always try those. I can resize a still image in MSPaint easily, but I'm not good with animated images or gifs. But I know there are options out there on places like Photobucket and Tinypic.
I'm sure someone a bit more proficient in these kinds of things will be along soon to give you a better answer. ^^