Running your furnace off one battery for even one day, most likely, it will run down to the point where your furnace will shutdown due to low voltage long before you run out of propane. The group 24 battery that was originally going to be supplied with my 32 buds has a capacity of roughly 1000 watts if 100% used but more realistically closer to 500 watts available for running a furnace. The LP detector would run the until the battery is nearly dead.
The furnace uses around 30-35000 BTUs of propane and around 130 watts of power(12v) per hour.
Dependent on temperatures, I have a 2016 32 Buds and have solar to charge my batteries and can monitor total power consumption.
I usually run 100% of my 12v off solar and batteries and have the convertor turned off most of the time. I have led lights for most interior lights and also use 120v for supplemental electric heat in addition to my furnace so your mileage may vary. I have run the furnace without shore power and supplemental heat. I usually can make one night but the batteries are drawn down by about 20-25% of their capacity if it is very cold out at all.
So here are some of my observations.
1. Powered down parasitic loads require around 100 watts per day (12v power). Parasite loads are anything that uses 12v even when supposedly in off position.
LPG detector is mostly the culprit in my case.
2. Refrigerator on propane and 12v. Nothing else but parasitic loads. 350-400 watts per day (12v power). Not connected to shore power.
3. Living in the weekend. Cold weather lows15-30 highs 32-45, 120v shore power connected. Electric heat is on and furnace running on battery/solar/Propane
1-20lb tank of propane used over 3.5 days. Furnace runs frequently but electric heat (1500w heater) is supplementing use around 1100 watts per day of 12v power.
I have 3 group 31 batteries in a parallel array along with solar charging the batteries. I can go about 3 cloudy/raining days before my battery array is run down.
I have about 4000 watts of battery capacity across 3 batteries.