If he were thinking about the supplemental draft, I think it would have been all over the news that he was working out for NFL teams.
I have trouble finding anyone who thinks Braxton is an NFL QB. His future would be at a position where he can run catch the ball, and not have to read and throw against NFL defenses. A position change for him at Ohio State would allow the 3-headed QB monster to become a more manageable 2-headed one, it would allow Braxton to do what he does best, and it would give him a season to prove his value to the NFL, and perhaps most importantly, an opportunity to show that he can stay healthy. Both Ohio State and Braxton would benefit.
It all makes too much sense for it to not happen - which is probably why it has zero chance of happening. :)