This is exactly how it will play out. If Cruz wishes to run, he won't have any problems.
No problems, except for getting vote from people who don't see him as being eligible or want anything to do with his politics.
I love the guy and think he's getting off to a tremendous start in the Senate!
But running him for POTUS will be divisive for the party that runs him, since those who like him but like the Constitution more won't vote for him and the other half of the country never would vote for him any way.
That sort of divide and conquer works against you if you want to win the WH.