I think it depends on how far you take it. White cowboys that are decked out look ridiculous. No real cowboy will be wearing RRL, or other boutique western wear, you will get no respect from cowboys if they found how how much it cost...of course a real cowboy would not care your label. I think subtle western wear could be pulled off by any person of any ethnic background.
I'm an Asian guy who wears jeans, denim or chambray shirt, Ariat cowboy boots and a Houston rodeo belt buckle to work every day.
I say go for it, but don't go overboard with rhinestone, bolo ties, waxed trench coat, etc.