My understanding is that the room must be reserved/in the name of the Annual Passholder (i.e., an adult) to qualify for the discounted rate. Like many other policies, the CMs may not adhere to it consistently.
FWIW, there are more perks available to annual passholders in 2002 (compared to last year). Might be worth it to get the AP for one of the adults in the party. Not sure how (or if) it would work to show child's AP to get perks such as 10% lunch discounts (at EPCOT and resorts) or 20% water park discounts.