Yes my battery is a power supply for the microcontroller. The power supply can come in 2 shapes, either from a 9V battery or from a 9V voltage adapter coming from the wall.

I was wondering, what will happen if i connect both at the same time, especially if Im using a rechargeable battery, that is half empty. the + and - of the battery and connected to the + and - of the interface to the voltage adapter. I hope im clear this time.
Thank you