I don't think the logistics make this ASB. (Why must people misuse this term? Is alien intervention really necessary to have Romans in Central Asia? Really?) I think a shared border situation could happen (Tang-style expansion plus Rome takes Persia, done), but any war would likely be a short and reasonably pointless affair for both sides. You wouldn't get an up-close-and-personal situation due to the sheer distances of their centres of power.
Plus, while I think that a Rome-China border is not impossible, sustaining it would probably be highly unlikely. So, there's probably scope for a few years of border, and some skirmishes over misunderstandings. But nothing big.
Although, the idea of a crazed (but fashionable, as well as militarily brilliant) Roman general deciding to march an army to China in order to wring the secret of silk manufacture out of them might be rather good. It would require a specific set of circumstances, and a specifically intense kind of individual (like, Alexander/Napolean level here), but it could be done.
Plus, while I think that a Rome-China border is not impossible, sustaining it would probably be highly unlikely. So, there's probably scope for a few years of border, and some skirmishes over misunderstandings. But nothing big.
Although, the idea of a crazed (but fashionable, as well as militarily brilliant) Roman general deciding to march an army to China in order to wring the secret of silk manufacture out of them might be rather good. It would require a specific set of circumstances, and a specifically intense kind of individual (like, Alexander/Napolean level here), but it could be done.