If I may quote Fulcher of Chartres, a Crusader historian writing around 1115
"Consider, I pray, and reflect bow in our time God has transferred the West into the East, For we who were Occidentals now have been made Orientals. He who was a Roman or a Frank is now a Galilaean, or an inhabitant of Palestine. One who was a citizen of Rheims or of Chartres now has been made a citizen of Tyre or of Antioch. We have already forgotten the places of our birth; already they have become unknown to many of us, or, at least, are unmentioned. Some already possess here homes and servants which they have received through inheritance. Some have taken wives not merely of their own people, but Syrians, or Armenians, or even Saracens who have received the grace of baptism. Some have with them father-in-law, or daughter-in-law, or son-in-law, or stepson, or step-father. There are here, too, grandchildren and great-grandchildren. One cultivates vines, another the fields. The one and the other use mutually the speech and the idioms of the different languages. Different languages, now made common, become known to both races, and faith unites those whose forefathers were strangers. As it is written, "The lion and the ox shall eat straw together." Those who were strangers are now natives; and he who was a sojourner now has become a resident, Our parents and relatives from day to day come to join us, abandoning, even though reluctantly, all that they possess. For those who were poor there, here God makes rich. Those who had few coins, here possess countless besants; and those who had not had a villa, here, by the gift of God, already possess a city. Therefore why should one who has found the East so favorable return to the West? "
Even by this early point, they were already starting to assimilate. It's not that hard to imagine them assimilating even more.