No, it can't be done easily.
The avatars are tiny little things... and while your suggestion's a good one (actually, a GREAT one), this software's a package deal. Every custom modification not only has to be done by a (paid) programmer, but it also has to be reconfigured every time there's an update, etc. We have learned over the years, that we pretty much need to keep such things to a minimum.
On the other hadn, there IS a spot on our profiles where we can post a larger picture. If more people would add a picture to their profile, it would definitely be very cool!