We haven't used the AP rates in awhile due to wanting our Loews upgrades. But we have been asked to show it 2x when we were actively using the APH rates.
Your chances are excellent that they won't ask to see the pass. But be forewarned that if they ask to see it and you don't have it, your rate will fall back to the current rack rate.
But the good news is - just tell them you have to run to guest services to pick up your AP. Upgrade it at guest services and bring the upgraded pass back to the front desk. You will then get your AP rate.
Do bring printouts of your confirmation of your AP rate. It is always smart to bring this with you in any case, as computer mistakes can and do happen. But in your case, if your rate gets bumped to the rack rate, you would want to show them proof that you had the AP rate previously.