It all depends on how it was wired. If your installer included an inverter bypass switch you would just throw that if the inverter quit. Or, if your generator transfer switch is installed between the inverter and the coach then the generator would still work fine with a bad inverter.
It is normal to have the inverter on to pass power thru it so no problem there.
If the generator feeds the inverter input and there is no bypass then yes, you would not be able to run off the gen if the inverter quit.
You just need to ask your installer.