I don’t think so
I dont think so either. Egypts government is a bitter enemy of Erdogans Muslim Brotherhood. Gulen is a guy on their side.
Egypt also cant be blackmailed like the US can, about Eurppe, Nato, Russians, Incirlik or Iraq. Arguably Gulen is safer in Egypt than here.
In Egypt he doesnt risk being handed over, though he has to worry more about assassins.