Without a way to recharge the battery, your furnace will drain it in fairly short order. For the stove/RVQue/fridge, as long as you have propane you are probably in good shape and you'd probably be able to get a couple weeks out of two full tanks. You'd need minimal power for the hot-water heater. If you do an LED light conversion, you'll be able to get good light with minimal impact on battery life.
As for keeping the battery charged, assuming you can't plug into the house or that house power is down, you will need a generator or will need solar to recharge the battery. A larger battery than stock (or a dual battery conversion) would be good as well.
If you do come up with a way to recharge your batteries, put in a 12v socket and inverter, or a 12v USB plug socket, so that you can recharge cell phones. Or pack in a small solar panel recharge kit specifically for recharging devices.
Basically, assume the most-basic of boondocky circumstances.
Because we largely camp without power and are planning a Burning Man trip, I am planning a solar conversion next spring with either dual golf cart batteries or dual Group31 12v batteries - assuming I can find the space for it all.
2012 Lincoln MKX
2013 Rockwood A122BH A-Frame