I suppose if the Turks want into the EU bad enough they might obey their own laws on this one. But maybe it has crossed their mind that under European law they would have to give Hagia Sophia back to the Orthodox ... among other things.
Yes, and for that reason, and the fact that the seminary and the Patriarchate would have to be opened to any citizen of the EU, the EP is, understandably, very eager to have Turkey join the EU.
It would clearly be good for the EP and the Christian minorities in Turkey (the Greeks in European Turkey, the Armenians and Christian Arabs in Asis Minor), but it's not clear it would be good for the EU, Christendom as a whole, or Western civilization to have Turkey in the EU.