To the best of my knowledge, no. Radical Chinese nationalism has always tended to be more pluralistic than its Russian counterpart, in part because many ancient Chinese empires weren't Han, and Han culture is one of the most absorptive on Earth. I know of a hardened Chinese nationalist who tells his kids that the Yuan and the Qing, while not "Han", were Chinese: it's hard to imagine an equivalent to that in Russia, where Ukrainians are considered Russian, full stop. (To give some current context to the difference between the two, while a hardened Russian Orthodox nationalist of the old school, Putin has for most of his reign been very careful to promote a Muscovite version of multiculturalism that celebrates all citizens of the Russian Federation, regardless of religion or race, provided that they give unconditional loyalty to the Kremlin. Putin has advisors such as Shoygu that are not fully ethnically Russian. This bears absolutely no resemblance to Merkel/Obama-esque notions of "celebrating diversity" and political correctness, of course, but the fact remains that Putin has largely locked up Russia's equivalent to Chinese or American ultra-nationalists precisely because their Russian counterpart is more vulnerable to ideas like this-Russian culture doesn't have the absorptive tendencies of Chinese or American culture.)

However, ethnic minorities had a really rough time of it during the Cultural Revolution-Hui Muslims were forced to raise pigs on the pain of death, all concessions to the Tibetans were suspended and the population as a whole abused, and Korean language schools were shut down in the Northeast due to China's poor relationship with North Korea at the time, for example. This wasn't so much done out of ideas of ethnic purity so much as the overall political paranoia of Cultural Revolution China-Beijing in those years literally wanted to set the world on fire. But this made China very vulnerable in its border lands with India and particularly with the Soviet Union, however, so it largely ceased in the early 70s when Mao halted the worst of the Cultural Revolution. The CCP after Mao's death did its best to mend relationships with ethnic minorities and even occasionally apologized and made amends, if mostly on the basis of pragmatism.

No, the PRC was founded on the principle of equality between all ethnic groups and the opposition of Han chauvinism. The PRC organized the different ethnic groups into the "55 nationalities" - the Hui ethnic group, for example, was constructed during the PRC, and gave them favorable affirmative action policies.

This is the 1954 English translation of the PRC Constitution:

All the nationalities in our country have been united in one great family of free and equal nationalities. The unity of our country's nationalities will continue to gain in strength on the basis of the further development of the fraternal bonds and mutual aid among them, and on the basis of opposition to imperialism, opposition to public enemies within their own ranks, and opposition to both big-nation chauvinism and local nationalism. In the course of economic construction and cultural development, the state will concern itself with the needs of the different nationalities, and, in the matter of socialist transformation, pay full attention to the special characteristics in the development of each nationality.

"Big nation chauvinism", or in Chinese 大民族主义 (a better translation would be big ethnic group chauvinism) is a clear reference to Han, since the Han ethnic group made up almost 90% of the population. The 1982 Chinese Constitution made it clearer by directly referencing Han chauvinism.