Some points:
1) I am in a long term interracial relationship, and we experience both deliberate and unconscious racism on a daily basis, be it from work colleagues, neighbours or children on the street. It's still a very terrible issue and the world isn't as politically correct or enlightened as people claim it to be.
2) Racism can work in both directions, something often ignored by the very vocal victims of it. Is it not just as racist to say the show should have actors of other races on it simply because they are of other races?
3) If you are judging Buffy from a modern attitude then you are wrong to do so, because you have to take into context the time period of the show. Things are hugely different now, a mere decade later, than they were in the late 90s. (Just look at how nowadays every teen has a cell phone, for example, whereas Buffy started out with a beeper. "If the apocalypse comes, beep me.") There were a few notable exceptions, even as far back as Shaft, soap and Oprah, but on the whole you couldn't popularise a show with an actor in the lead role who had a different racial background than the racial background of your target audience. Supporting lead was the best you could usually get away with. TV shows are all about making money, so if you couldn't make it popular with your demographic then you simply couldn't get the show made at all.
4) Buffy is a show that helped change the world. There is a rather direct line that can be followed from the 60s feminist uprising, to Sigourney Weaver's Ripley, to the Spice Girl's chant of "Girl Power" and then on to Buffy kicking ass on mainstream television. Each step changed the world just enough so that today we find it horrible to imagine that at one time women were relegated to roles of either love interest, sex object or damsel-in-distress. Singling out that it didn't also combat racial stereotypes is asking too much. Change comes in little steps and Buffy helped take on one war and win it. Applaud it for what it did do, not condemn it for what it didn't.
That's the long answer. The short answer to would it have been as popular a show with an actress of a different racial background in the lead is "No."