There are a few Asian origin pilots based in the US flying for US carriers but most if not all are "Americans", i.e. US passport holders.
My theory is that aviation is not something that Asian communities worldwide find to be a viable career. Until recently, there are usually one major airline per country in Asia and if you don't make it then you are out of option. And majority of those do hire mostly ex- air force personnels since private training is cost prohibitive for most.
To dedicate your time and study for something that's very limited in opportunities is not something Asians like to do.
Much more options in the business, engineering or medical route. They are also viewed as a more respectable and face lifting career.
Language is another barrier that keeps a lot of Asians from pursuing aviation career overseas (not in there homeland). Like a lot of controllers in Asia, many can speak technical English providing that they have learned and rote memorized or something that they have heard and used before. Try requesting something that's slightly unusal and that radio will go silent for a noticable period of time. Similarly with native Asian pilots.
Unfortunately, the first road block for them would be the technical interviews. Hard to wing it with just sheer hard work and knowledge alone.
With volatility in the aviation industry worldwide, post 9/11, I don't see any changes in Asian's attitude towards career in aviation/ pilot as something viable and mainstream in the near future.