No, they do not count. A Theocracy is ran entirely by an Ecclesiastical/Clerical government, where power comes from religious mandate. For instance, the United Kingdom is not a Theocracy, despite the fact the Monarch is also the official head of the state religion. Why? Because the monarch's religious power is an addition to, not the source of, their secular authority. A Theocracy is ran solely through religious means. About the only modern example where the line seriously starts to blue is Iran. They are technically both a Democratic Republic and a Theocracy, however the religious & secular powers are split between two individuals, which means it isn't a "true theocracy".
Basically, a theocracy is where governing power is dictated by religious or spiritual reasons, rather than secular and temporal ones.