Probably.
It's almost certainly some kind of a browser caching issue; browser that is behaving in normal manner should request the file only once per page load.
If it did perform separate requests every time it came across the tag then you'd have different picture on each post, but that's not normal for browsers, and it would be highly stupid from technical standpoint; it would slow pageloads (all of them, not just the ones related to my avatar) to a crawl and stress the servers unnecessarily.
As far as the browser is concerned, there's only picture. It loads the picture, and uses it every time it gets referenced on a page. Even with caching working as it's supposed to work - regardless of how aggressive it is - you should still see only one avatar per page.
But whatever, it's not big deal if it wants to load moar cats.
obesebear: LOL, indeed.
