I don't think there's an easy answer to that question, because it depends a lot on who ends up taking the reigns in the Zhongshe Party, and then how intelligent/forward-thinking that person, or those people, are. Unfortunately we don't have a lot to work with when it comes to the wider views of the Aisin-Gioro who survived the early Republic, especially considering the ideological framework later imposed by the CCP. We can't use the views of, say, Pujie post-1949 because his views had likely been substantially altered by the CCP's system of prison "reform".
However, I think we can extrapolate two most-likely outcomes.
1. The Manchu leadership is aware that their ethnicity and style of government leaves them politically vulnerable, and so they make genuine efforts to rebuild the country and reform along the lines of a constitutional monarchy. From a purely logical perspective this makes sense, since it's probably the only way the monarchy could survive in the long term. The Manchu coup's success is already a stretch even by alternate-history standards, especially if you assume the Manchu are actually successful in surviving the Japanese invasion and asserting control over the rest of China. The primary problem with this route is that it isn't really clear where the initiative to undertake such a wide-ranging series of reforms would come from. Perhaps Pujie, since he's younger, maybe less fixed in his ways, and bears a wider range of experiences than the remaining aristocracy? That's going out on a bit of a limb, in my opinion. Perhaps Zaifeng, who from what I've read seems to have actually been a decent person? That's tough because he seems to have hated the burden of leadership. Maybe someone else? I haven't looked into the extended Aisin-Gioro family, so I can't say for sure.
2. The Manchu Party leadership isn't aware that their ethnicity and style of government leaves them politically vulnerable, and so they resist attempts to reform, leading to stagnation and inevitable revolution. Basically Xinhai 2.0. To me this seems a more likely outcome, since the majority of the remaining Aisin-Gioro seem to have been a mix of out of touch and unwilling to truly lead. Monarchies can, in theory, be very effective at taking decisive action, but to do so they require a decisive leader, which in 1936 the Manchu don't seem to have.