If dry camping it will use up your battery pretty fast.
Much faster than your propane.
The furnace blower and control circuitry uses about 7 amps of DC when running.
If the furnace runs 30 minutes in every hour it will consume 3.5 amp hours from your battery's capacity every hour (OEM battery has about 70 AH typically and some small campers may have even less)
A Fresh completely full 70 AH battery will last 20 hours with only that as the draw. You will be going to bed after using lights, fridge, parasite draws like radio and propane detector, etc all day and without recharging it before bedtime, you may wake up pretty cold.
Obviously if it is colder it will run more and warmer; less.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW