300 or so watts is about right for an absorption fridge on AC power. That's about 30A DC input to the inverter, roughly speaking. Your engine alternator and battery isolator typically ought to be able to keep up with that level of demand (though the recharging of a discharged house battery would be significantly slowed). Without the engine running, of course, you're very limited in battery capacity with this load, at about an hour realistically. All in all, I think running the fridge on propane is a far more practical idea.
I'm not generally in favor of wiring an inverter to power the entire 120V AC electrical system on an RV, rather than just switching over selected circuits. In addition to the converter and perhaps the fridge, you presumably would want to disable (or try to remember to turn off) the electric water heater element, if you have one, and the air conditioner.