Not knowing how robust the charging system in the AP is and if it can handle over-voltage I would not exceed 5V . I put to together an external battery supply / charger using a BEC (battery eliminator circuit) which is capable of taking 6-23V input and supplies 5V out put at up to 3 amps.. I use this with LiPoly 3cell 2.2Ah batteries which I have many of which I use for radio controlled electric aircraft.
In board AP battery is nominal 4.2V X 4Ah =16.8 watt hours.
My 3S 2.2A ones are nominal 12.6X 2.2Ah=27.72 watt hours. Thing is I have many of these and with my charging setup it only takes me 20 min. to charge one.
AAs are less than 2Ah useable capacity so not really a great idea unless used with a BEC and if you have a bunch of rechargeable ones.
One of my battery test post.
http://forums.x10.com/index.php?topic=25135.msg141623#msg141623Hint: Those figures were with a fully charged internal battery at 4.24V and external was only maintaining this charge level. As the voltage goes down more amps. are required to produce the same amount of watts.