....hmmmm....it's a bit of a stretch I believe. There are first generation immigrants and then there are second generation immigrants and thereafter. I can assure you, second and above do not see themselves in this light. As far as a first generation Chinese immigrants are concerned, I would say there is a sentiment that is different from the 2nd and beyond, in that they are more culturally tied to their original culture. But not in the way you describe it. And, more similar in degree to the European immigrants of the past.
Of course the sentiment will diminish the generations go on, because each successive generation is exposed to more American culture and more distant from Chinese culture.
But comparatively speaking, given equal generation immigrant, the Asian immigrant will always be proportionated more self-identified with the country of his origin, and this is probably true for 3 or 4 generations before this effect becomes negligible.