I tried this - even reset it back to factory. Now, instead of silently draining my battery, my iPad makes this frequent sound, like "Bit" in the original Tron, saying, "No! No! No! No! No!" over and over again. I think I will simply stuff the keyboard in to an envelope (or, very likely, the original packaging, which may be in my closet) and send it back to Apple, c/o Tim Cook. Maybe, if they receive enough of these, they'll get the message.
As a side note: I had the iPad docked in the keyboard while it was making this sound. I placed an AA battery behind the iPad, to change the position of the iPad slightly. This did stop the noise. Keyboard still didn't work.