Yes, AAA Members can purchase and print the attraction ticket online. 
You can click on Purchase Attraction Tickets from the drop down menu under Travel.  Once on the Purchase Attraction Tickets page, you have some options.
1) You can click on the Buy Online buttons under Walt Disney World Resort, Universal Orlando Resort, SeaWorld Parks Orlando, Busch Gardens Tampa Bay, LEGOLAND Florida Resort and More Attractions, where a new window will open to log in.  Once on the attraction tickets purchase site, choose the attraction, choose the ticket type (adult/child), choose how many, Add to Cart and then Checkout.  You will receive an email once payment has been processed to print your tickets.  Follow the instructions in the email to print your tickets.1
2) You can click on Movie Tickets, Concert Tickets, Sports Tickets and Other Attractions & Show Tickets Buy Online buttons to access more attractions, sports, concerts, events, etc.  On the next screen, click on and then click on Find Tickets green button.  You will be asked to sign in to access this feature.
To go purchase attraction tickets, click here.

1If you have any issues with the actual purchase of the attraction tickets, you can contact their Technical Support staff at 321-282-6625*. 
If you have any issues with your user id/password, you will need to contact AAA's Technical Support at 877-736-7813.

* Technical Support is available by telephone 24 hours per day, 7 day per week. Technical Support Agents cannot provide park specific information such as hours of operation. Technical Support Agents cannot provide detailed information about the entitlements associated with tickets and passes. Technical Support Agents cannot provide detailed information about events. Technical Support Agents cannot approve or process refunds under any circumstances.