Yes. Trump's challenge allowed 0bama to produce his latest fake, and point to it as genuine, while the MSM validated it, took a bow and said "I told you so". This was done to head off movements in several states to make candidates - not just 0bama - produce proof that they were qualified to hold the office. Now 0bama can point to his latest fake and state that this is his proof. Election officials in each state will be too timid to question validity of this fake, and 0bama will be on the ballot.
The REAL responsibility for forcing a candidate to prove their eligibility lies with Congress and the Electoral College, although I doubt you'll see any of the lilly-livered cowards in those bodies raise the slightest objection.
I am not so sure that this is true about the states. The states may still require that each candidate show an official copy of their birth certificate to the sec. of state in order to qualify for a spot on that ballot.