OTL, not a whole lot. While he can push south into China, he'd be fighting a plethora of warlords, some of whom were pretty competent. The Ma clique and Yan Xishan come to mind. For him to be more successful, the Whites need to first win the Russian Civil War, and then lose the peace. First part would require a great amount of good fortune where the White armies coordinate their offensive to nullify Trotsky's 'defeat them one at a time' strategy. The latter, however, is very likely. Without the Bolsheviks as a unifying factor, the white movement will fragment into Social Revolutionaries, republicans, monarchists, etc.
A world where both Russia and China are reduced to warlord states is a state where Ungern-Sternberg can thrive. I can see him bringing the Buryat, Tuvan and Altai lands under his rule, and then some.