Actually no. On an individual basis sure, but not on a mass scale. Poltical control of territory almost never implies inbreeding. For "ethnic groups" to mix there has to be a movement of peoples that permantly settle among the locals. In Greece Turkish settlers did arrive, not on a mass scale though, and they didn't settle among the locals. The communities remained seperated even as late as the early 20th century. Religious differences being the most important factor. One can not say the same for the Slavs, that mass migrated during the 7th century reaching the Peloponeese. They settled among the locals and got tottaly assimilated in 1-2 centuries. Same with the orthodox Albanians, the Arvanites, that settled in Attica in the 16th century. They got assimilated pretty fast.
Again the same with the orthodox Vlachs, a branch of the Rommanians.
But with the Muslim Turks, no. We did pick up many habits from the prevailent Ottoman culture, though and vice versa.
In your thinking then Brittain and France were half-Roman when the Germans migrated.