No, it does not. Regardless of whether he is a NBC for President, he meets the qualifications and requirements to be a US Senator, one whose responsibilities is to assist in providing advisement and consent of nominees- including a Supreme Court Justice.
I am going to vote for Trump in my primary and for Ted in the general if he gets the nomination. But this issue argument is specious and completely diversionary, IMO.
Totally bogus argument, Cruz is a sitting US Senator and as such he represents the people of Texas and the people of Texas will have their say in who gets seated on the Supreme Court.