YES....running it on 12V DC will drain a battery very quickly. That is why the 12V DC is typically used while traveling so vehicle can charge battery as it is being drawn on.
When on shore power the converter along with battery can provide/maintain the 12V DC draw but mos folks use the 120V AC heater when on shore power or propane.
Propane can also be used while traveling.
Fuse/wire.....minimum 10AWG wire with 30A fuse. Any voltage drop will really affect the performance of 12V DC heater (probably a 150W heater---which can pull 12.5A)