I found a script online which lets me confirm that Unity will work just fine with my computer (I think I found it on OMGU! if anyone needs the link I'll add it) but when I try to log in using Gnome-Shell the system hangs badly, even when doing things as simple as trying to browse my applications. Is it possible that I would have problems running Gnome-Shell even though Unity 3D works fine?
Yes, it is possible. Gnome Shell uses Mutter whereas the standard Unity uses Compiz. Since they're different solutions, they have different requirements with regards to drivers. That means Unity might work well and Gnome Shell not, or vice versa.