Yes the USPS does allow AA batteries too be sent through the mail.
USPS allows batteries such as AA, AAA, D and any other small batteries to be sent through the mail and even cell phone batteries or laptop batteries are okay to be sent through the USPS mail.
The only types of batteries that USPS doesn't allow to be shipped through them is car batteries, truck batteries and other large batteries.
You can also send batteries such as those for battery drills etc but just no large car batteries etc.
AA or other small type of batteries are okay to be sent through the USPS.