Does the XBox 360 Play and Charge Kit work with normal AA batteries?

My 3 XBox controllers now hardly take batteries at all, whether new or old. Can I also use the Play and Charge kit cable with a normal AA battery, since the kits with battery are hardly available anymore? Or could I simply modify a USB cable so that I can supply my controller with 3V via the normal battery compartment with contacts?

You can't insert batteries into the Play and Charge Kit.

It consists of a battery (in the form of the case where the batteries normally come in) and a charging cable with which you can charge the battery or play completely without battery or batteries.