I think one thing you need to understand is that the rise of nationalism was frequently anti-clerical and anti-religious. The French Revolution proclaimed "the citizen" to be sovereign, rather than the king, whose sovereignty was divine. Napoleon would popularise the idea that "citizen" was a legal category for political recognition and representation by/for the state, which was a single community.
Contrast this with Ottoman law. Each millet (literally, "nation" in Turkish) was a community governed by its own legal traditions across the Empire, with a designated representative at the Porte (be that the Sheikh al-Islam, the Patriarch, the Apostolic Nuncio, etc). It was a nationality law that was, by nature, not territorialised, because the Ottoman Empire was not territorialised; it was expansionistic, hence pluralistic.
So, no. The millet system is not something which could serve as the basis for a civic nationalism. The Patriarch of Constantinople was the Orthodox millet's "ambassador" to the Porte; he represented the "nation" within the greater "Empire." Bishops and church leaders in Greece, Serbia, etc may (and often did) encourage to partake in a greater Christian struggle against the Muslim enemy, but this did not mean that there was no differences or power struggles between their congregants, or even within the clergy. The institution of the Orthodox Church played an enormous role in the Greek and other Christian independence movements, but don't think this was a conflict between the Rum Millet and the Muslim millet. The Greek Orthodox Church was a major part of Greek nationalism, but the Filiki Etera was still a community of liberal, mostly French-educated intellectuals, many of whom were devoutly anti-clerical.