Jahja (wiki link) could never claim the throne of the Ottoman Empire as a Christian. It's just not possible. What might happen is the creation of a hostile state in the Balkans but one that will probably collapse after he dies and is no longer around to beat up the Ottomans militarily. If however he can kill all the Ottoman family but himself so there is no legitimate pretender, you will probably have the empire fragment into a few powerful states for a while with Jahja's state being just one of a number and probably unstable as the Balkan Muslims will probably rise for the Muslim states if Jahja's ever shows weakness.
Basically I think a weaker Ottoman-Style muslim empire because of less of the Balkans is possible if everything goes right. Austria will probably benefit from this quite a bit.