Roger. I have a 3000 watt, xantrex sine wave inverter. I can turn on and off, the inverter and the charger. I assume, you have an inverter/charger.
If I have the Inverter turned on, it will supply power to everything, except the A/C's and Water Heater. When I start the genset, or plug in to shore power, the transfer switch goes to the shoreline, and the inverter will shut down, still showing that I have it switched on. If I have the charger section switched on, it will charge the batteries while on shore power or Gen power. When I shut down the genset, or unhook the shore power. the inverter takes over and the transfer switch will revert to inverter. I can also put it in Safe Mode, but then I have no power to anything, even if plugged in. Even with no load, at all, the inverter takes a little power, but not enough to make me shut it all down. I usually never have a no load condition anyway. DirecTiVo won't record anything if it's not running...
If you have selected the inverter "on" option, it will not be on if you are plugged in.
It may have an option to shut down the charger section too, but not sure, but when you are plugged in (or running the genset) it will either be charging and,or not inverting.
As for the Microwave, If you have a sinwave Inverter, and it's big enough, by all means, heat that coffee or TV dinner, it Won'thurt it a bit. Mine sounded a little louder on the Modified Sine wave I use to have, but it never quit. I'm sure the manufacturers check to see it the things they are adding to their coaches, will work with MSW inverters or not, I mean come on, imagine the warranty claims