You just hit on the dilemma I alluded to in my first response, which I call the "Chico Marx Effect." I love Chico Marx and I hate Charlie Chan, and I have no satisfactory rational explanation for how that can be because conceptually, they are both doing exactly the same thing. Chico and Charlie are both people putting on makeup and affecting an exaggerated accent, mostly for a cheap laugh. I don't think either one had malicious intent in mind. And yet I like one and not the other.
The easiest explanation is, "Chico Marx doesn't look like me and Charlie Chan does," and in all honesty, I can't completely rule that out as the root reason. However, there are characters like Amy's parents on Futurama or "Miss Chinglish" in the Black Lagoon anime who are much closer to Charlie Chan than Chico Marx, but I think they're both hilarious. I may also have a conceptual issue with Phil LaMarr voicing Samurai Jack, but his voice (and the light accent he lends to it) has never once affected my enjoyment of the show.
Besides, if a character is a fully realized, interesting character in his or her own right and happens to be non-white, then I'd say they're not a token character even if they are the only representatives of their race in the cast. To me, a token character is a character whose one and only purpose is to be "the black one" or "the Chinese one." Everything they say and do is tied to being black or Chinese or whatever. Even though someone like Wade on Kim Possible is the one of two black people in the regular cast, I still wouldn't call him a token. He's a fun character to do stuff with that happens to be black, but he doesn't get any special treatment, good or bad, because of his race.
A boring character is a boring character no matter what color they are, just as a good character is a good character no matter what color they are. I also think that your question has the implicit idea that you have to use race as an explicit or integral part of a character to make them interesting, and I don't think that's true. If anything, I think that's how you end up with token characters on shows.
I find it a bit more likely to call it an attempt, however misguided, to acknowledge that Chinese and Indian people are entering the American professional workforce in greater numbers.
-- Ed