Well considering that the MBA uses an 18volt charger (if I remember correctly), that means you would need at least 12 AA batteries (that's 1.5V per AA * 12 = 18). That's a whole lot of batteries.....
Also the Apple MagSafe and MagSafe 2 are proprietary connectors so you can't use a third party adapter (at least it isn't legal to sell you an adapter by a third party using the Magsafe connector) and Apple doesn't currently make a AA battery charger for the MBA....
No, you can't do that. AA batteries are not compatible with the charging technology that Apple uses, involving the built-in battery, the MagSafe adapter and the Mac's logic board.
The link below should answer most, if not all, of your battery/charging questions. If you haven't already done so, I highly recommend you take the time to read it.
It should be possible to put 11 AA batteries in series to make 16.5 volts and connect it to a MagSafe cable, but with a capacity of 2500 mAh it wouldn't last too long. It might be a better idea to use D cells and get about 6 times more capacity.
I've been meaning to try 3 x 6 volt lantern batteries in series to see if it powers a 15" Mbp (18.5 volts)
The. MagSafe cables are readily available on ebay if you don't have a dead adapter to cannablise.