When you say 'Roman Empire,' you are being ambiguous. Which Roman Empire? There was one Roman Empire that used to worship idols of Venus, Mars, Ceres, et al., and then, there was another Roman Empire that had a distinct and contradictory religion, that shunned idolatry and espoused monotheism. Make up your mind. When you say 'Roman Empire,' I have no idea what you are talking about. In the context of Christianity, no Byzantium is not an offshoot of the Roman Empire; if that were true, Byzantium would have also worshipped Venus, Mars, Ceres, et al..
BTW, here is a Temple of Bacchus, and example of Roman religion, for you:
The classical Roman Empire
I am sure the Roman Popes would have strongly disapproved of this.