The offical policy is a "valid annual/seasonal pass required at check-in". I've never been asked to see the pass (one time I was even asked if I needed park tickets), but a lot of people have.
I had this happen to me last year. I told them at check in I was going to be getting my new AP later that day. I showed them the expired pass and then showed the desk person the new one later that evening when I returned from the park. No problem at all.