I don't think the administration has ever actually formalized an opinion on avatars. I've stated my opinion in the topic Monolith cited, in addition to Disguise and Fquist.

If avatars are uploaded to the JCF, they would use extra bandwidth. This would be negligible though. A maximum 2KB uploaded avatar combined with a signature reduction to 500 bytes would result in a net gain of 500 bytes maximum per user (the current signature limit is 2KB). Even if we kept signatures at the current limit, that would only be a total of 4KB per user and I doubt it would cause significant bandwidth problems. Images are also cached by browsers, unlike signatures.

There is no option in (this version of) vBulletin for remotely-hosted avatars. It would be too difficult to enforce size restrictions on them anyway.

Just to (re)state my opinion: I'm in favour of allowing avatars, if reasonable limits (such as 2KB and 48x48 pixels, and no animated images) are put in place. I would also be in favour of smaller signatures, maybe with a maximum of 500 bytes.