Probably not. The Russians lost control of that after Barbarossa, when Sheng Shicai (the warlord in charge) attempted to side with the KMT.
I have no idea why when people talked about Republican Sinkiang, they always focus on either Sheng Shicai or the Hui warlords, as if they were capable of controlling Sinkiang on behalf of the KMT. In reality, they represented only a tiny minority whose grip over Sinkiang was shaky at best, nominal in most cases, and were very unpopular.
In 1944, even when the RoC was still an ally with the USSR, Soviet agents provoked a revolution in northern Sinkiang, and established a second "East Turkestan Republic" after horrendous ethnic cleansing of local ethnic Chinese.
Nor did USSR "lose control" over the rest of Sinkiang. Rather, Stalin deliberately betrayed Sheng Shicai to Chiang Kai-shek when the benefits brought by RoC's alliance with the USSR outweighed the values of Sinkiang.
Once the Soviet Union get back to its feet (when they defeat the Germans, and turn their red juggernaut against the much weaker RoC), she would certainly once again try to expand southward. Once Mao's rebellion turned sour for the reds in China's Northeast, I don't see anything that could stop Stalin from giving some Mosin Nagants to Sinkiang's "freedom fighters", or send some "Internationalist Warriors" there as well.
The actual invasion would be similar to Russian Invasion of Georgia in 2008, only more brutal and on a larger scale: the USSR gives Soviet passports to secessionists in Sinkiang, and when the KMT troops try to fight these insurgents, the Soviet Army would launch a long-waited invasion in the name of protecting Soviet citizens. The invasion, headed by armored divisions, would destroy the defenders at ease. Within weeks, a new Soviet Socialist Republic would be added to the Soviet motherland.