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IMO, that's a bad idea for several reasons:
1. If server hosting the avatar is slow, that will slow down rendering of the whole page.
2. You don't have any control over the filesize of the avatars; someone could link to a 1MB image file.
3. It's a security risk. An link to an embedded image can embed Javascript in the page that could steal cookies, hijack the session or do other bad things.