There is a bit you can do that is free. CloudFlare, for instance, will improve things for you with your images. It may not solve the problem completely but will save you bandwidth and get your images to your users faster.
Well there are several variables. Uses can insert full size attachments, so that would bypass that. If they didn't insert the full size attachments, then the thumbnail version will be used; if you use the out of the box image processor (GD), this will only be the first frame. If you use ImageMagick, then this will be an animated thumbnail and thus can still potentially be sizeable.I was actually expecting attachment images to be thumbnailed and loaded that way until clicked. Is this not the case?