It'd be a historical curiosity and likely nothing more. However, there is one slight chance it might have more impact if contact is prolonged.
China interpreted Rome (or Daqin as they called it) as a counterpart to China, but on the other end of the world. If China continues to idealize Rome as a counterpart to themselves, and frequent enough contact is maintained that Rome is something more than a legendary realm, then it is possible that China's view of international relations might be more advanced than the simple "everyone is a vassal to the Middle Kingdom, and all embassies are tribute embassies" system China employed. Instead, they might be open to treating representatives from the dominant European power as an equal in protocol. That might make China more open to Western explorers in the 1500-1900 period and reduce the tensions that came along with Chinese treatment of European embassies.
The idea of Rome as an antipode to China has a rather Daoist ring to it, doesn't it?