Due to to loss of cores and government rank, there would be no reason for that decision to be made. In-game, the Conquest of Constantinople resulted in the release of Morea, rather than the demotion of the Byzantine Empire. Morea was a tributary of the Ottomans, not quite a vassal by the game's standards, but not quite fully independent either. There was no particular reason why the Despot of Morea couldn't claim imperial pretenses, other than as not of offend the Ottoman Sultan. If a rump Greek state survived in the Peloponnese, and it was semi-subject to the Ottomans, there is no reason why it would not claim continuity with the Byzantine Empire.