Both of the above answers are correct. It will really depend on the CM you get at the parking booth.
They have every right to charge you the parking fee as the free parking perk only extends to an active AP, not a voucher. As safetymom said, pay the money and bring the receipt to the Guest Relations booth when you activate. They will refund the money.
OTOH, you may encounter a sympathetic CM who will just wave you through. So be prepared for either eventuality.