Sorry for the delayed response. We have a few Facebook accounts that range from 50 to about 500 friends. We don't see any loading issue with that amount, but it does look like Facebook tries to load all the user's avatars. I just checked out how big one image is, and it's about 2.5kB. Assuming this is true for all of them, at 1000, that would be about 2.5MBs to download, which could definitely cause bandwidth issues.
However, each of those images are loaded through an iFrame, which means that they should be loaded sequentially and shouldn't prevent the page from continuing to load.
Can you try on our demo site and see if you have the same loading issue? We have invite module with avatars up there, so hopefully that will help narrow down the issue:
sourcecoast.com/jfbconnect/demo/jfbc-invite-full-view
Let us know what you come up with, because we don't have many suggestions, unfortunately.