Yes he will. The courts will toss those bills because individual states don't get to rewrite the Constitution's eligibility criteria, and thus, those bills are unconstitutional and cannot be enforced.
In their idiot birther enthusiasm, Nebraska and Arizona have overreached and thereby snatched defeat from the jaws of victory. It would be perfectly sufficient and constitutional simply to require candidates to produce documentation of their birth. In Zero's case, that would mean he would be required to waive his Hawaii privacy rights and allow the Hawaii DoH to cough up all that it has. Then, if the results appear not support his eligibility, that would be a separate federal, not state, case.
Presidential candidates are required to provide evidence they are Natural-born citizens in order to be placed on the presidental election ballot. A natural born citizen is a citizen born under the jurisdiction of the United States to parents who are Citizens of the United States. The secretary of state shall:
(a) Verify all candidates satisfy this criteria
(b) Remove any candidate from the election ballot who fails to satisfy this criteria