as far as i know the batteries cirtuit is isolated when u plug the ac adaptor. so u would have to mod it to be able to charge and play at the same time.
but, as far as i know ni-mh bateries are chraged with higher voltage and and pulsating current to avoid internal cristalization.
so it's imposible to do a easy mod to the gp2x for that. you would need a dedicated ic to charge/discharge/isolate the voltages, make a miniature board and then fit everyyhing inside. without it you would fry the console, like with cars, that you have to disconect the battery to charge it because you can fry the instruments if not
ps: that wallwart seems like some kind of marketing scam. like those MONSTER GOLD hdmi cables
and those 3100mAh batteries are a scam also. the maximum for a ni-mh AA cell is ~2600mAh. And those have a defect that is its high internal discharge.
the only ones that i would recommend to use are the precharged ones, like the sanyo enerloop and the sony cycleenergy. that even though they are rated at about 2000mAh, as they have a difrent voltage curve they last almost the same. plus they can be without use for many mounths and still be able to turn the device on.