O Wren wrote, on Mon, 22 Dec 2014 08:41:32 -0500:

With this being the week of Festivus, good luck with that...LOL.

What you could do is open the hood on your generator and measure/record
the battery voltage.

Then disconnect the ground lead of the battery, wait 24 hours, and
measure the battery voltage again.

If the battery voltage drops after being disconnected from the generator
for 24 hours, the generator obviously has a grid-powered charging
circuit.

Capeesh?

Is this "Oren"?

Anyway, I was dead wrong and all you guys were right (as usual).
I called Generac at 888-436-3722x2(consumer)x2(existing product)x2
(permanent)x3(all other)...wait...

The lady who answered said instantly that all the built-in generators
are charged from the "T1" wire from the house.

She said the "T1" wire was blue or white and went in behind the
control panel. She didn't know the difference between 120VAC and 12VDC,
but still, she was sure that the T1 wire fed the battery.

She said when it exercises, it doesn't generate any power.

So, based on that, I was dead wrong.
The built-in generator charges the battery from the mains.
I was wrong.