I think I'm going to have to say no to that. Having to query whether or not each player has uploaded an icon or not upon each generation of the page will probably slow things down even more. Also, many players are already uploading custom icons anyway.
The player icons are cacheable for 24 hours, so your browser will only make requests for them at most once per day. (This means if you upload a new icon, other players won't see it for 24 hours unless they reload the page). I'll probably increase this value later once most players who want to upload an icon have done so.