Not sure, I do know whenever theres a popup window of any sort, my game goes to desktop screen and crashes FFxiv.

I would suggest either you get one of those Play & Charge kits which will allow you to recharge your gamepad while playing, or what I did and got my hands on a Wired xbox360 controller.
http://www.komplett.no/k/ki.aspx?sku=312862

I think thats your best bets, cause I would assume everytime you need to swap normal batteries, your game will have to be restarted.