That's half correct. Indeed, the vast majority of Greek speakers did adopt Islam and were subsequently linguistically Turkified. But although they are Turkish speakers today, their culture is no different than the culture of Greece and other southeast European countries.
I imagine that if the people of modern Greece had also adopted Islam, they would have eventually abandoned the Greek language and embraced Turkish instead. Nevertheless, the culture (e.g. food, music, art, architecture, way of life, values, etc) wouldn't really change. Basically, instead of having Greek speakers taking credit for giving birth to Western civilization, you'll have Turkish speakers claiming ideas of liberty and democracy as their own. In other words, the Islamization of the remaining Greeks would lead to the linguistic Turkification of these Greeks, but the culture will remain intact, as was the case after the religious conversion of Anatolia, the Caucasus, Egypt and the Levant.
I mean, this is largely the case. Until the rise of Turkish nationalism at the turn of the century, the Ottoman Empire largely saw themselves as the heirs of Rome. Especially around the coasty bits, culture was (and in many ways still is) closer to Greek/Mediterranean than that of other Turkic-speaking groups which the Young Turks decided were the "proper" Turkish culture.