No, it does not, and no, you cannot. It is a magneto engine with no capability of adding a charge stator. Best bet for light battery charging is to get a solar type that sits on the seat.
I can vouch for the little $30 solar "charger"It only maintains the battery, but I have one that has kept my 5 year old
really tired lawn tractor battery holding up even sitting 3 weeks at a time and through the north east winter.