Wouldn't Mandarin being the language of the Elite mean the Communists are less likely to choose it to prove they're not just a new wave of Elites but rather the Common Man's government?
Nope. LeX is not saying that Mandarin is perceived as the language of the economic or social elite (e.g. landlords), which might indeed be something the CCP would oppose. But Mandarin was the language that the majority of the elites within the Communist Party spoke, and as such I see no reason why they would choose anything else as the language of their government. Maybe if the TL is structured in such a way that, for whatever reason, the top echelon of the Party is composed almost entirely of people with a different native tongue, you could see the Party using that language as their default, especially if they only control the area in which that language is spoken. Even here, though, as said above, there is something of the idea that Mandarin is "the language of government". Even the Communists here tend to be quite nationalist, and there has been a push towards Mandarin going back to the late Qing Empire. In those days, the Chinese armies were divided up by language/ethnicity (which, admittedly, was something of a necessity in days of such low literacy, when most soldiers from the south couldn't understand Mandarin, and those from the north couldn't understand Min Nan, etc), and this was seen as one of China's weaknesses. They might even be right, given how little the army and navy of nothern China helped the south during the war against the French, or how little the southern armies and fleet helped the north in the Qing-Japan War. Regardless, there was something of a push for more linguistic uniformity, and many people saw Mandarin as the natural choice, even if they themselves did not speak it (well), because of its prestige and the fact that it was the language of the majority of the national population. Really, as i said above, the only way i see that changing is if none of the governing elite or the population in the controlled territory speak it, and even then I think they might pay lip service to the idea of Mandarin as part of their claims to be the real national leaders of China.