As far as I know the stator is just for ignition, not for charging a battery. It works like this:

The stator creates electrical energy from the magnets in the flywheel passing the coils that make up the stator. It sends this to the powerpack which stores and changes the voltage from AC to DC volts. The trigger, also under the flywheel sends a small voltage to the powerpack depending on the flywheel position, this releases the stored electricity to the coils which step it up and on to fire the plugs. The battery is only there to turn the motor over, it has no play on the ignition system.

However, if you have an alternator it is right there with the stator, part of it.