The sure fire method is to go to Downtown Disney to buy your AP and then go to the park.
People have reported mixed results going to the park first, you might be let in but then you might not. They would send you on a big U turn back towards DTD. One person was able to get reimbursed for the parking fee at the moment of buying the AP.
You have to admit, if you were allowed to park free with just the voucher, they have no way of knowing you will actually get the AP that day.
Disney hints:
http://members.aol.com/ajaynejr/dispass.htm