This is where the Indo-Greek even Kushan analogy comes from.. Yes, they have converted to Buddhism, Shivism, etc and mixed with the Indian culture. They can wear Hindu marks on their head, wear Indian clothings, etc. Fight the Indian way, eat the Indian way, etc, but doesnt make them any less of a foreigner.
Did the Machus mix with the Hans? I heard in the beginning the Machurian emperors are a mix of Mongols and Manchu hybrid..
You see, that is the part you lack history about China.
Manchu has been part of minority tribe in northeastern China. During late Song Dynasty, they became very strong and overturn the Northern Song Dynasty. They set up themselves as Jin Dynasty (which is also part of Chinese history). The remaining Song officials escaped to the south China establishing Southern Song Dynasty.
Jin wanted to invaded Southern Song Dynasty while Southern Song Dynasty wanted to reclaim the Northern Song Dynasty. Each wanted to be the heaven-granted son of god, or ruler of China. While none has beaten the other.
Then Mongolian became stronger and there came Genghis Kan. Mongolian and Southern Song worked together to overturned Jin. and Later Mongolian's Yuan overturned Southern Song to reunite the whole China.
Manchu fell into pieces after Jin was overturned but there came another great leader for them: Nurhachi, centuries later. He and his sons took advantage of later Ming dynasty's peasant uprising and overturn Ming. So Manchu in China really established two dynasties even though the two are several hundred years apart.
Today there is no much difference between Manchu and Han, even though you can get better opportunities when you claim you are from minority, e.g. education, jobs and etc.
The marriage between Han and non-Han Chinese are very common. For someone who are complete Han Chinese looking, he may be half minority from either parent side. However, we view all of them Chinese and never think them foreigners.
The power of Chinese culture is that we can assimilate any outside culture or people into china and finally they become fully Chinese. We did not use force to do that all.
They may still remain their original religions, e.g. like Muslims, or totally assimilated, e.g. there were a lot of Turkish people inside China thousand of years ago, before that, even the Huns. A lot of them went west, e.g. Attila the Hun, or Turkey... Those who choose to stay were assimilated into Chinese culture and are now part of Chinese.
So in Chinese blood, it definitely consists of different racial background. Even the Tang Dynasty, the founder Li Yuan was also thought to be part of Turkish. However, he adopted Chinese name, took Chinese tradition, took Chinese position to become army soldiers, then generals and later took his chance to became emperor and found the strongest empire then. So he is fully considered as Chinese. So he may be part of Turkish descendant, who care? We Chinese always view him Chinese and I think he never doubted he is Chinese either. He also called him heaven-granted son of god, which was used by every Chinese emperor no matter which dynasty it is.
So Chinese culture is a multi-racial culture even though later no matter which racial background they may come from, they all tried to call themselves Han Chinese since they are the majority. But in reality, the Han Chinese is very much diverse.
That is why we have always viewed Jin, Yuan as well as Qing part of Chinese history. In reality, each successor did the same to take over and adapt.
No matter how different initially they may be, if they choose to stay, they all become Chinese and was accepted as Chinese as well, indeed nobody forced them either. Those who choose not to normally have gone somewhere already, like some of the Turkish as well as some of the Hun.