I think the short (or at least technical) answer is no. I don't think anyone could argue against Christianity being incredibly important, even fundamental, to the history of the Byzantine Empire, but you could argue either way as to whether it is a theocracy.

I suppose it depends what you mean by theocracy. If you mean that the state is ruled by religious figures, then no. The Emperor was the ruler of the empire, supported by a bureaucracy of civil servants and had authority over the church. However, (s)he was not a church official (bishop, patriarch etc).

If theocracy is a state ruled by the laws of a religion (or church) then definitely no. While many Byzantine laws (certainly in the later empire) were influenced by religious considerations, the majority stemmed from the secular (or even pagan) principles of the Roman Empire/Republic. The church certainly didn't have an official role in creating or enforcing civil law.

However, you could argue that Christianity was so entwined with and fundamental to the Byzantine Empire's character and history that it is a theocracy. Without their staunch Christianity, the Byzantines history with the Muslim invasions, Crusades, Iconoclasm, heresies and the church councils would read very differently, if at all.

And I suppose with that, there's a possible line of saying that the Eastern Roman Empire wasn't a theocracy but that the Byzantine Empire was. At that point, though, we're debating the point at which the Eastern side became it's own rather that just the Roman Empire (or at least part of it) and I think that's leading us away from a meaningful answer to your question.

This was my first attempt at answering a question on this sub. I'm just an amateur Byzantine enthusiast so I understand if this post doesn't meet the standards required here.