generator battery charging?

It's just like your car - the battery recharges whether you have the headlights on or not.

Let me Guess a Generac? What a POS that is, Yea I ran across one on a very expensive piece of emergency equipment, Coroner brought it in to get the battery changed on the generator because it was dead, So after having to literally disassemble this POS to even get to the battery, I see the POS doesn t even have a charging coil wire coming from the case where the flywheel is let alone a diode tree for a rectifier, But rather a little 1/8" jack where your suppose to plug in an external 110v battery charger, Seriously? Then who ever built this overpriced rolling refrigerated corpse condo did have the foresight to put an onboard battery charger for the interior lighting batteries as long as the generator was running, but the generator was neglected in they re engineering department, Meaning it didn t charge at all, But you see I have connections, They have money and I have mad skills and knowledge, That s why I make the big bucks, Now everything is maintained by a solar battery tender and all batteries are charged while the generator is running,

OMG, it charges its own battery as it runs

It depends on whether it has an alternator or built in battery charger. With the latter it must be under load.

It depends on the model.

Mine recharges while it has a load.