Bill, we cannot tap into the battery bank when on shore or generator power. The choices are shore, genny or inverting.
With the engine running, I will run an air or two as we have four alternators. But, the genny needs exercise and why not run that baby! At 4.5 yrs. of ownership, we have about 380 hrs. on it.
On the new Liberty's, my understanding that the power sources can be shared if needed. The new ones have the Volta Lithium Ion system which allowed them to reduce the size of the genny to a 12.5K Onan.
Safe travels!
MM.