I think they are pretty close to that now. The Chinese have been flooding the province with their own Han people for quite some time now - just as they did in Tibet.
You can say that for almost all 50-plus “nationalities” within China’s borders. Actually, Turkmen make up one of the groups considered as Uighurs. Also included are Hui ethnic people. The Communists determined there were only five ethnic groups that made up China (not the 50-plus number I cited). However, Shanghainese, like myself, do not consider ourselves as part of the Northern Chinese who rule from Beijing.
In fact, one side effect of growing wealth among Chinese minorities is greater demand for self-rule and decentralization. A weakened central government means a less influential Communist Party, which is something many minorities can agree upon.
Within the design and engineering profession in Chicago, I have worked with Uighurs, Tibetans, Poles, Bosnians, Albanians, Armenians, Pakistanis, and Indians. The only person we all had a hard time with was a Taiwanese who served in the Imperial Japanese Army. None of the Muslims was dogmatic about religion; two of the nicest Christmas gifts I received while working at one firm were from a Bosnian and a Pakistani.