To a certain extent, yes and particularly for Jews. After the reconquista the Ottoman sultan offered the Jews of Spain the chance to resettle in the empire. A great number of them took up the offer, which resulted in a flourishing Jewish community in Constantinople.

When Zionism rose to prominence in the 19th century Ottoman Palestine likewise became a destination for Jews, particularly those fleeing the pogroms of Russia and Eastern Europe.

I can't think of any large scale migrations of Christians to the empire, however, if that's more what you had in mind.