Well, I do not think it would be possible. The logistics are simply too disadvantageous for a large scale military campaign. Not to mention that Rome had a pretty good army. They'll also have naval superiority in the Med. The chinese army might at times have been more technologically advanced, but didn't it suffer from a lack of discipline and corruption?
Also, the chinese didn't really want to conquer. Meritocracy meant that nobles with crazy ideas of conquest didn't get very far.
The only way I could see it happen would be if China had a Qing dynasty style population boom during the Han dynasty. If the chinese spread west (unlikely due to the environment), they could populate large areas, and thus provide the logistics base necessary to support so many troops in the west.