This is a self-answering post: if the picture below is moving, the answer is "yes, animated gifs do work". The only remaining question is for Stephane, about whether they work in blogs, too.
Hmph. I guess not. Dangit. @stephaneb!
Would Gibbs recognize this?
Indeed, you cannot upload a gif animation. I looked at the code and it wouldn't be straightforward to support it. What you can do though, is upload your gif animation to imgur or other server and then simply copy and paste the url of the animation where you want it in your post. It seems to work.
Thanks for checking, and for the suggested work-around.