I don't think a Chinese monarchy necessarily has to liberalise and democratise. The People's Republic of China is plenty successful as it is. I could see a successful Chinese Empire functioning superficially like the KMT or CCP. The Emperor would be mainly ceremonial and the head of the Grand Council would be the prime minister. Democracy in China could be similar to democracy in the People's Republic of China, where the people vote to confirm the centrally appointed politicians and elect a largely powerless legislature. If economic conditions are good and the Chinese government remains popular, they would have no need to cede any power to the people or opposition politicians.
Problem is that by the 20th century it would be very difficult to keep a monarchy in power in China AND have China be successful. There was too much republicanism in China at the time. The Taiping Rebellion and its aftermath might've been the last time for a successful Chinese monarchy, just have one of the victorious generals revolt, depose the Qing, and get proclaimed Emperor like rumour suggested might happen. They'd still have a huge challenge ahead of them in terms of reforming the government and playing Western powers off each other.