A lot of problems with this chronology. Rome was just coming off of the Hannibalic War and the Seleucid empire was alive and kicking, so there is virtually no chance whatsoever in even the wildest fantasy scenerio that this could have even happened.
On the Parthian side, the Empire would not yet be what you might think, as MithradatesI would only a few years later set the path that would make the Parthians an Asian powerhouse. Also, the Parthian military did not become what we think of it as being until Mithradates II defeated the Scythians and incorporated them into the army.
I am going to be fair and say that at no time could this alliance crack China (at least not when they were at their best). You can find literally dozens of Rome Vs Han Dynasty threads on Historum and all over the interest. I don't really have interest in arguning it anymore. I could see Rome doing very well in some kind of fantasy scenerio in which 10,000 Romans take on 10,000 Chinese on neutral territory, but regardless, I do not believe that even if they added the 40,000 or so cavarly that the Parthians could have offered and good quality infantry archers and slingers, that they could ever have done any damage to a country that could field, what, 600,000 to 800,000 troops of mostly high quality? And it would be a logiistical nightmare.
Have fun. I predict this thread will go about 47 lines. I have stated my opinion, but may jump in to refute some of the nonsense that is going to come up about how Romans could not defeat cavlary, Romans could nto defeat mounted archers, Romans did poorly in Asia, etc. Nonetheless, in this scenerio, China and not even close.