I have worked with Asian teachers, and had two directors of studies too. It depends on where you want to teach; in the UK, and I imagine this would be fairly similar in a society like Australia, it is quite common.
There are Asian teachers working in many countries, though you do hear stories about finding it harder if you don't 'look the part'; I believe you might find it harder to get work in, say, some of South Korea schools, where I have heard stories about their preferring teachers that conform to stereotypical views of native speakers. In some places it might be seen as an advantage though. Where I am living, one of the most successful institutes is Singaporean, so it's not a problem here. That's not to say that this is universal, but I know enough Asian and other teachers to say that it can be done.
I'd check out any country carefully first- there are race issues in some countries. EnglishTeacherX says in his blog that racism is on the rise in his city in Russia and that he feels a lot less comfortable there than he used to, and he's a white American. However, there are plenty of places where it will be no problem.