I have heard that the present day Greeks are largely the descendents of Germans and Slavs who came in during the barbarian migrations.
Germanic people didn't make it that far until the Middle Ages, and even then they did not settle in Greece in large numbers.
Many Slavs, Turkic groups and Bulgars did settle in Greece, however.
The Greeks of the classical period may have been more "Germanic" (a meaningless word at that time, maybe "Northern" might be better) than the peoples who took their place.
Greece is an ethnic melting pot, unified by the Orthodox faith and its liturgical language.