To answer your question simply, yes BJ can beat GSP. BJ has arguably the best ground game from his back in MMA, probably one of the hardest to deal with guards, great TDD due to him being able to balance on almost nothing, very good stand up, and a finally improving gas tank.
The question now comes is GSP better in all aspects or in just one or two? Stand up is actually hard to call, GSP seems to have a better arsenal but BJ has a rock solid chin and strong hands. On the ground GSP does not seem to like to be on his back at all so probably the best thing BJ could do is try to end up on top somehow, but most likely it will be BJ on his back and GSP in his rubber guard that can quickly turn into 4 subs.
I think either one can win, I still haven't made my choice on whom I am betting on though.