Well, I do not know if the Roman Reconquest would have been feasible if an Osman state had emerged in the 14th century. There is a reason that Constantinople came to be feared by Europe again by 1567 at the Battle of Belgrade. For a short time it looked like Constantinople might occupy Vienna, in the East she reunited Anatolia with Lebanon and much of modern Kurdistan and Armenia while in the West she took Sicily by utter surprise and even managed to briefly occupy Bari, Otranto, Calabria, and Apulia. Had Isaacius V or Basil VI been more patient or diplomatic the Empire might still be alive. Unfortunately the Austrians and Hungarians actually united their thrones and began their own Reconquista, eventually overrunning the whole of the Empire under Joseph II just in time to face a monsterous threat from France and the kick-off of the First Revolutionary Wars. Constantinople has always been the City of Men's Dreams and remains paramount to commerce in that part of the world even today, no wonder the Austrians sought to colonize it so heavily.