I would not suggest hooking up the inverter to the main power input for the RV, simply because there are too many things to remember to turn off when you're using the inverter that you want to have on when you're using shore power. This includes the converter, the fridge AC element, the water heater AC element, and most any other electric heater.
It's not that it can't be done or doesn't work, it's just a good bit of hassle and a rather rapidly discharged battery bank if you forget something.
A better approach is to have only selected circuits switched to the inverter, or dedicated to inverter power. If you don't have a large power draw on the inverter circuits, leaving them dedicated isn't a big problem when you're on shore or generator power because the converter will supply sufficient power to the inverter to prevent the batteries from being discharged. This has the nice side effect of not causing the TV or DVD player reset itself when you switch power sources.