For the furnace you need 2 things, LP must be on and you need 12 volts. If you don't have a battery your converter may not put out 12 volts, mine doesn't, other converters do put out 12 volts without a battery. If your 12 volt interior lights work then you are all set. Just turn on the thermostat. The blower should start and then the furnace will self ignite and after a minute you should feel heat out a vent near the floor.
Let us know if that does/doesn't work.
Gene & DW Ginny
2002 Sunline T-2363
2008 Toyota 4-runner 4wd 4.7L V-8
Reese Dual Cam straightline - P3 Brake controller