With the modern high efficiency inverter/chargers now available the effeciency for all load ranges from zero on up is sufficiently good so as to be relatively negligible in terms of energy wastage. In fact, if one needs a shore
charger (ostensibly you do or else you wouldn't have the
battery bank to drive this thing) the technology called "bidirectional switching" is what makes inverter/chargers so good. If you need the
charger you almost get the
inverter function "for free" or vice-versa. Here we are considering the latest switch-mode technology in that charger-only switch mode units cost almost as much as an inverter/charger.
As mentioned before, a
generator is not needed for heavy intermittent loads or light continuous loads...that is what an
inverter is best doing. Save the
generator for heavy continuous loads where it is optimally loaded.