I'd say earlier than that. The Turkic migrations into Central Asia began well before the Mongols, as early as the 6th century with the Gokturk empire.
A weaker China (say one riven by civil war) would likely have been seen as an attractive target to the various groups of Turkish nomads, and might have pulled them away from Central Asia. Alternately, China could have crushed them like they did the Xiong-nu. Or the eastern Iranian horse tribes could have remained fairly powerful, containing or even rolling back the Turks (at one point Indo-European peoples migrated as far east as the
Ordos area of Inner Mongolia).
Once the Turks break out though, Central Asia is just kind of screwed. It doesn't have defensible terrain, and is wide open to attacks from any horse-based pastoralists from the north. So you'd need to find some way to strangle the Turkic migrations before they left the cradle.