Can theocracy co-exist with democracy

Yes, it can. For example, if only one religion is allowed in a country, and if oficials of this religion have some power, but where people still have a say in the government, then it's a democracy and theocracy at the same time.

In a way, UK can be argued to be theocracy and democracy: its upper chamber of the parliament has many Lords Spiritual, which are Bishops of the Anglican Church, but the lower chamber is elected democratically.