Hmm this is a fairly difficult thing to assess, especially considering the limited number of primary sources available describing Sino-Roman contact at all, much less their awareness of contemporary politics. Volum 88 of the Hou Han Shu gives a Chinese account on Roman society while Pliny and Seneca also write concerning Chinese trade (particularly on silk, which both bemoan as degrading Roman morals by allowing women to walk around in transparent clothing), though they wrote centuries before the Han collapsed. Given, however, that the first alleged Roman embassies to China only took place in the mid-2nd century and mid-3rd centuries (right on the precipice of Han's devolution to the 3 Kindgoms), it is unlikely that the Romans were aware of the shift in political power, as they delivered gifts to Cao Rui of Cao Wei as gifts for the "Chinese Emperor" much as they had for the previous Han emperors, and continued Byzantine trade with China in later centuries makes no ready distinction between Chinese dynasties, just generalizing the region and its people as "Seres", "Serica", or "Sinae". While traders closer to the Chinese edge of the Silk Road may have been more tacitly aware of the shift of power in China, and such info may have disseminated down the Road to Roman traders, it is unlikely that the Romans had much awareness of (or cared about) Chinese dynastic politics.