No. The ONE for iPad & Mac does not charge AA batteries when connected to AC. You will have to use a separate device to recharge your batteries.
No. When the ONE is running off of its internal batteries and connected to an iPad, iPhone or iPod touch, the iDevice runs off of the its own internal battery and the ONE runs off of its internal batteries in a neutral power state.
Apogee highly recommends using rechargeable NMiH ( Nickel -metal hydride ) batteries for 2 good reasons. 1. They last about 2 1/2 times longer than normal non-rechargeable AA batteries. 2. Rechargeable batteries are more environmentally friendly in that they are used over and over again for a long period.