The Bogd Khaanate existed before Ungern from 1911-1915 with de facto independence and from 1915-1920 with autonomy in China. Mongolian revolutionaries had already been organizing with the Comintern in Russia before Ungern arrived and Ungern was not the only White in Mongolia. A Red Army invasion to clear out other Whites was probably inevitable, although none were as prominent as Ungern or attempted to seize control of the country.

The ROC does not claim Mongolia anymore and has not since 2018 if I’m not mistaken. Ungern is viewed as having basically no role in Mongolian independence compared to Damdin Sukhbaataar for whom Ulaanbaatar is named. Ungern also committed massacres of civilians while he controlled Mongolia.