I can't say what would have happened to the Roman Empire if they continued in the the prominent pacifistic tradition that seemed to be present from the beginning of Christianity. Maybe the empire would have fallen far sooner than it did and God would have used their dispersion to spread the gospel to the ends of the earth much sooner than it would have otherwise been spread. Maybe God's hand would have been on Rome and would have protected it from destruction and the Roman empires pax Romana would have been extended ad infinitum, so long as they followed God and used his prescribed means. Maybe Christians would have found that they had to abstain from government service, leaving the secular citizenry to run the army and legislature, and letting them bear the sword. I don't know. Certainly sheathing the sword as a country seems like it's a death wish. But then again, assuming such has two significant problems.
First, assuming that using means of God which are foolish means destruction fails to trust God. Daniel prayed in the open and was fed to lions. Daniel's three friends failed to bow to the king in public and were thrown into the furnace. Gideon was told to whittle his army down to a few hundred men. In all of these cases, God provided protection and salvation for his people.
Second, assuming the Roman Empire would have been destroyed if it didn't use the sword places the goal of action on the wrong thing. The goal of using God's means is not preservation of our lives or preservation of a kingdom in which we like living. We use God's means because he tells us to. We use God's means because it sanctifies us. It builds faith. If non-violence is the means to which God calls us, what does it matter if our enemies overthrow our kingdom? Won't we then have more opportunity to show the best imagery of the gospel - enemy love? Is our obedience and our desire for love and the gospel to shine even if it is at the expense of our own life and our country's standing?