- Yuan Shikai IOTL believed the Qing dynasty was done for and wanted to hijack the republican revolution for his own ends.
- The OP envisions him putting his money on the Qing instead.
- IMO, anti-Qing sentiment was widespread but not severe to the point that the empire was actively collapsing. The revolutionaries who would attempt to lead the republican government, after all, were a small group of southern Chinese expats who jumped on a very spontaneous and ill-organized movement.
- Since the Qing wasn't actually in chaos in 1911, it's not implausible for Yuan Shikai to defeat the revolutionaries and maintain the Qing order for a few years.
- The rebellion would probably fail.
- Yuan Shikai would be even more powerful after this.
- Constitutional reforms would go on for a longer time, which is a good thing since it gets officials more used to following rules (at least on paper).
- More simmering regional unrest in the south, probably a bad thing but bound to happen anyway, at least if you believe that warlords are a probable outcome by 1910.
- Yuan probably doesn't try to set up his own dynasty, which is certainly a good thing.
- Major revolts are probably staved off for some time, but a combination of fear and lack of real power vis-a-vis Yuan Shikai are going to have the Manchus making more and more concessions to the Han.
- Yuan probably dies before 1920 (IOTL he died in 1916).
- The Beiyang army probably takes a hit with Yuan's passing, but in a different or less divisive manner as IOTL due to butterflies caused by the lack of a bogus dynasty to ruin its cohesion.
- If a strong leader is able to take the reins from Yuan after his death, we may either see
-- a stable military dictatorship with the Manchus left as a powerless figurehead
-- a military dictatorship with some republican/parliamentary pretenses
-- some combination of the two.
-- a northern military dictatorship that may or may not support the Qing in name, pitted against nascent southern revolutionaries allied/controlled by local military governors.