The average income in China was depressed by colonialism and then by Maoist communism, so the Chinese have a big gap to overcome. They've certainly been working on that gap, but it's not going to be easy to break into the rich club now. Some aspects of China will hold it back, such as corruption, zombie companies, and property laws that are less than favorable.
I would guess that its massive size will also hold it back. Can that many people become rich? It seems to me that income equality is the more likely outcome. Just look at the rising income inequality here in the US.
Extras. Based on a less-focused Brad DeLong article. Also, look at the difference between being rich on average and being rich at the median.