3Tinks, that's what I did - I paid for the AP online and then took the paper to the turnstile. They gave me a paper ticket that said "Annual Pass" on it and my name, and that worked to get FP's until I got my actual card. I didn't use it to park hop, but I'd assume it would work as a hopper, since it said "Annual Pass" on it. I think the only rule is that you have to get your real card before you leave that day. It would be easy to just ask the CM that takes your piece of paper.
Also, if you are getting a Premium AP, or another AP and adding on parking, you'll have to pay for parking that first day when you show up with your print-out, and then they'll reimburse you the $14 at the AP processing center.