No, JFBConnect doesn't store profile information directly. It uses other profile systems, as there's plenty out there and a lot of other extensions already integrate with them. We focus on Facebook integration, but for profile integration, we let other's who focus on display and that type of thing.
With that said, however, Joomla 1.7 now comes with a profile plugin built in. We already support it partially, but we'll be releasing integration to automatically import into those fields later this year, which we're hoping that other extensions will start using to pull profile data (just like they do with JomSocial, CB, etc). Unfortunately, the User Profile plugin doesn't currently support avatars. We're very hopeful that it will in Joomla 2.5 (due in January) or shortly thereafter, as once it's there, that will likely become the main profile system that everything integrates with.. which will make us very happy
It's possible there's already another plugin that adds avatar support to J1.7 that's gaining steam, but I'm not aware of it... it shouldn't be that difficult, in all honesty.
Hope that explains.. but in short, no, we don't do what you're looking for.. yet. We agree though that JomSocial is overkill for just profiles, which is what a lot of sites use it for.
Alex