I haven't had to show my AP when I've entered the park using the AP discounted MHP tickets in the past. I looked over the ticket's fine print and it doesn't say anywhere you need to show proof of a valid AP at entry. However, it doesn't say you don't have to show the AP either. So, based on the past, you'd probably be okay, but things could always change (without notice). You will need a valid AP to participate in any AP exclusive activities (last year they had a special AP treat trail).