They won't, and even if they did, it wouldn't be effective. Taiwan still calls itself "The Republic of China" and would still claim Tibet and Xinjiang, even if they did somehow end up ruling the Mainland again. Also, Hainan and the former Manchuria have no interest in separatism: Hainan is almost entirely Han and the provinces that make up Manchuria have a similar percentage of Han to China as a whole, and the Manchu language has only a few thousand mostly elderly speakers.
Hainan has a decent sized non-Han population(~25% being the estimate by everyone but Beijing), and even then, most of the island’s culture is a bit different from the mainland’s. Nonetheless, I didn’t call those two particularly feasible - just possible.
As for the ROC’s claims? Yes, but if it allied itself with Uyghurs, Mongolians, and Tibetans, I can imagine that some form of confederation could reasonable be established.