I'm quite sure they do. As a black woman I've dated men of many different race. I recently dated a Lebanese man for 4 years and an Afghan for a year before that. I think that the only issue I had was a culture clash. The Lebanese man I dated felt that his family would did not aprove of me because of my race and religion.
I have no problem with them at all. Blacks girls have a stereotype of not really liking anyone. I can vouch that that is not true. I think a lot of middle eastern people are gorgeous, they're so slept on.