Nah, I think even if Ted Cruz looked and sounded like Cheech Marin they'd fuck with him. Same way they fuck with Ben Carson. The good Dr. Carson's definitely on the insane side of conservatism but he also looks and sounds like a black man...a black man from Detroit no less. Also, I think that a majority of black people my age were at one time given a copy of Gifted Hands as teenagers. And if you were black and from the Baltimore or DC area, he probably spoke at your school at some point. He's actually unlike a lot of other black figures in the party in that I think that most black people had a very positive opinion about him until he started talking about his politics and in the process disrespecting our president.
And conversely, I think that had Barack Obama been the conservative Republican US Senator from Illinois they would have championed him in 2008 in the same way that they may very well champion someone like Marco Rubio next year. I think they get a kick out of someone that's not a white man speaking their language, which is why that one black sheriff from Milwaukee is on Hannity every time I've flipped by.
Again, even the most hard headed bigots tend to allow for there to be "good ones" who are "not like other [insert maligned group]." The fact that Ted Cruz doesn't actually speak Spanish probably makes him more relatable to Republicans or whatever. But I think they would lose their shit if there were say, a person that came illegally, was deported, but found a way to come back legally and now extols the virtues of the Republican party, truth, justice, and the American way for any audience that can scrounge up his considerable speaking fee.