History abhors a vacuum. Someone would definitely step into the vacuum left among the Eastern Orthodox. Even if only informally. Contacts between the Eastern and Western branches would increase significantly. Its not like borders were sealed in this time period. Without religious leadership with in the Empire the local priests will turn to their local Bishops instead who at the very least will be able to maintain at least informal contacts at least with their western counterparts in Italy, Austria, Hungary, Poland and the Danubian and Russian principalities.
While Russia is not a threat at this point. The Pope is still a formidable figure at this time and there are countries that could make life difficult and could now have added impetus to do so. I am not saying they would do any better, but I don't think we can automatically assume that greater conversion to Islam would result. If anything you could just as easily have a polarizationbetween the Christians of the Balkans and The Porte without a Patriarche and emmissaries fromthe west will certainly make greater inroads insome parts of the Balkans.
I also doubt that the Greeks would be that easy to convert, Orthodoxy is in some ways central to their identity. Certainly one of the Greek Bishops would assume an unofficial leadership role even if not sanctioned by the Ottoman authorities. It would be dangerous for Ottoman authorities to try and suppress even an unofficial Orthodox leadership. It would antagonize the populace and revolt would become commonplace especially among the Greeks at the very least.
My own thoughts would be that this makes eventual unification between Eastern and Western Catholics more likely and changes significantly the Reformation. Indeed it may not even occur or it will occur in an entirely different context. Even if this didn't occur I think you would likely se a greater penetration of Catholicism in Bosnia and Serbia
That is a really big what-if but plausible.
however, I try to look at the past to see if history might repeat itself.
The whole Roman East, Africa & Asia Minor were once christian. Yet, scarcely 400 years after the conquest they were so muslim not even the crusade could change that.
There were churches too throughout this area. The Syriac, the Coptic, etc, but that didn't stop their adherents from converting no? Also at this point, the muslim world had enormous contact with the west. Yet I don't think that attempts by the patriarchs at Constantinople manage to change the religious situation of this are, nor the pope in Rome.
I think that, left without the patriarch in Constantinople, the balkan christian would
probably form their own churches like the Monophysite in egypt, etc, but that would not really help the tide of turkification of the balkans...
There again there is the religious strife among branches of christianity...then as well as now. To say that the pope would convert the balkans is a bit far-fetching, I think. after all, Grand Duke Notaras said he would prefer the turban than the tiara...and there is a big hostility between orthodoxy & catholicism, until now...
