They could choose who they want to identify themselves with. The Thai Chinese have a lot of Thai blood, but they identify themselves with both Chinese and Thai. Some Singapore Peranakan identify with China, because at that time, even though China was weak. These Peranakan refuses all the suduction of white man and serve China.
Below Robert Kho Seng Lim is a Singaporean Peranakan, he identify with China. He was the father of China's Western Medicine and the first Chinese fellow of USA academy of Science. He was the top medical scientist and top doctor at his time. He was a general in the China's army.
Below is Gu Hongming, another Peranakan, No 1 expert in western classics of China, a genius. He is a Chinese + white woman bastard. Today, such people will identify with white. Then the oversea Chinese are so patriotic that he identify with China.
Mao harm oversea Chinese. Also, Mao destroyed Chinese culture in a barbaric way. Today, oversea Chinese visit China and see a bunch of wolves who like to backstab one another. We also see low moral values, and a lot of sexualization of society, We get really quite disappointed.
The thing oversea Chinese can look up to China is probably shinny buildings. Without that, oversea chinese may despise china like what oversea indians despise india. Nevertheless I would like to say China has indeed build up a lot of respect and prestige in recent years, because of her growth in many areas.