Yup, you sure can, at any Disney venue that accepts Disney Dollars. Of course, you can't use DD$ to buy stuff online or by phone.
I paid for my AP with DD$ in December at the EarPort store in Orlandi International Airport. The airport stores, however, are run directly by WDW and are not part of the
Disney Store chain (which was bought out last year and is now operated by Children's Palace).
If you want to buy a WDW AP, you can get vouchers online at
www.disneyworld.com, or by phone at 407-WDISNEY. The only places you can turn in these vouchers for your actual AP (which is commonly called "activating" your AP) is at a ticket window or Guest Relations window at the four WDW theme parks or Downtown Disney, or at the Ocala Disney Information Center on I-75 in Ocala.
You can buy activated APs at several locations in Orlando, including the two Disney stores in the airport, the two Disney outlet stores at the Belz malls (north end of International Drive), the Disney outlet at Orlando Premium Outlets on Vineland Avenue, and the Ocala Disney Information Center on I-75, and of course at any ticket window or Guest Relations window at the four WDW theme parks and Downtown Disney.