The received wisdom in academia is yes, although several users here (Dimitris Almyrantis and Dimitra Triantafyllidou) have questioned how feasible this is. The argument made by Speros Vryonis Jr, and summarised in Nick Nicholas’ answer to When and how did modern Turkish become the majority in Anatolia?, is that any deurbanisation and mass migration happened in the first century after the Seljuk arrival, at the end of which Anatolia was still substantially Christian. The reduction of the Christian population accelerated in the 14th and 15th centuries, and was accompanied by extensive Islamic missionary activity. By the start of the 16th century, Western Anatolia (Anatolia Eyalet) was only 1.5% Christian.
Northern Anatolia (the Pontus) and Central Anatolia (Cappadocia) seem to have been exempt from this trend; Vryonis does not discuss these, but presumably the former is to be explained by the late conquest of the Empire of Trebizond, by which time the Millet system was established and gave Christians some degree of autonomy. The Christian population in Cappadocia was small, and substantially assimilated linguistically, and this may have been more an issue of inaccessibility.
Thrace is not covered in Vryonis’ work, and my impression is that a substantial Christian population remained in place.