Entirely unlikely. I've read stories about Roman legions supposedly captured by the Parthians after the Battle of Carrhae in 53 BC being used by the Parthians to garrison their Eastern territories and therefore encountering Han Chinese troops, but those stories are very unsubstantiated. By the 100s CE Rome and the Han dynasty certainly knew of each other, and the Book of the Later Han mentions Roman envoys reaching China in 166. Roman goods reached China and Chinese goods reached Rome, through intermediaries. However, there was no sort of prolonged direct contact between the two great Empires, and they certainly never "almost came to blows." Persia was in between the two great powers, after all.