That... doesn't really work, because there was a point where Christianity was made the official (and then later, mandatory) religion of the Roman Empire.
One thing I think a lot of people don't understand, is that the Roman Empire never "fell", it eventually dissolved and broke up into pieces. Nobody conquered Rome, it's just they eventually ran out of money and resources when their empire got too big for them to properly manage and it just went downhill partly due to corruption, partly due to laziness.
In fact, there's a lot of people out there who compare the USA to the Roman Empire because of the same reasons. Look at our infrastructure, our roads, bridges, education system, healthcare, corruption in the government, debt, etc. Can you honestly say that this nation is healthy now, as it used to be, say 50 years ago?
The USA has gotten lazy and lax about maintaining its infrastructure, and kinda like the Roman Empire, that will be its "downfall".
Remember Nebuchadnezzar's dream about the statue and Daniel's interpretation of it. Babylon was the golden top, Persia was the silver chest, Greece was the bronze lower torso, Rome was the legs of iron.
But yet, there's one more piece of this statue that will emerge, and it is made out of iron, but mixed with miry clay. It will be "like unto the last" but yet not as strong. It will be somewhat like Rome was, but not anywhere near as strong or powerful. This, IMO, could possibly mean that the regions that were once under the Roman Empire will band together in some sort of loose union that is kinda-sorta like an Empire, but yet nowhere near as strong and unified.