Only if you're black and have a conk. Which involves straightening. Which means once it's straightened, anyone can theoretically get it, so in fact that makes no sense. Cotten above seemed to manage, and there's lots of white people with kinky hair. Many Jewish guys, for instance. I'd mention Matt Stone as just one easy example, at least before he cut it off.
And need I mention that one reason black guys in the 30s and 40s got it, at least according to Malcolm X(who famously once sported one, when he was a hoodlum), was to seem closer to white? If your skin was light, you might be able to pass for Latino, some thought. And from many photos I've seen on graduations from the 20s and 30s, it was a pretty popular look at one time anyway. What was strange about Osborn was that it was a dated look by then. The fact Nixon had it was an indication.
That's the trouble with sweeping racial generalizations. It only takes one example to screw it up.