A theocracy is not a monarchy so it must be a democracy?
If the theocrats are elected, then yes, most definitely. You are still operating under the false understanding that a Republican form of government is somehow incompatible with the democraric principles of holding elections and electing people to represent us. Perhaps you also fail to understand that there is direct democracy and indirect democracy and that we are the latter here in the USA. Do the American people elect representatives or not? We are therefore a democracy. The people we elect are, supposedly, bound to limits established in the constitution. Since we are not an oligarchy or monarchy or dictatorship, we are a republic. Since our elected officials are limited by a constitution, we sre a constitutional republic. Since we elected those representatives, we are also a representative democracy?