Most RV converters are wired right next to the 12v and 120v distribution panels.
However
12v loads when not plugged in do not run through the converter. The converter is like a charger whose alligator clamps are on the battery, but the power cord is not plugged in.
With Inverters, some RV's have automatic transfer switches. I cannot claim any familiarity with these devices or their specific method of operation. The Inverter should never power a converter. Unplug it / flip the breaker for it, if there is a concern that it will be powered by the inverter.
Think about it, the converter is a battery charger. the inverter is a battery depleter. using one to power the other on the same battery bank at 85% efficiency on the 120v to 12v and then only 855 at 12v to 120V, simply wastes battery power as heat.