Indeed you can! I've even used the AP of different people in our group to get the discount, the only time they care about the photo on the AP matching the person who uses it, is when you're getting in the park (and even then it's barely a concern).

I'm thinking of the "Long Game" discount, spreading the benefits over the course of two different stays of 5 days per stay, considering that many local area hotels also give discounts to annual pass holders (The HoJo, most specifically)...