agree with tenbear above.
If the genny is out of fuel, it will still crank.
It does have both a preheat and a prime cycle, depending on what you do with the button. UP will prime, hold it there for a while if you suspect it had run out of fuel.
Down will preheat until it is preheated, and then will crank it. If it has fuel it will run if it cranks.
Your inverter should power many of your outlets and all your home entertainment. This should be seamless, and just happen regardless of if you are plugged in or not.
The "house" as well as the inverter, run off those 4 six volt batteries you posted about.
The "chassis" will run off one or more 12 volt batteries.
Most likely, a coach of that caliber will have a huge relay and a system of some sort to connect all the batteries together, so they all charge when you are driving and they all charge when you are plugged in.
