Plugged into shore power..converter supplies 12V DC system.
Furnace fan runs on DC power so you have DC.
Whether you have enough DC voltage is the question.
Furnace fan has to run at 75% or better of rated speed in order to make up 'sail switch' which allows DC power to circuit board for gas valve & ignitor operation.
What Brand/model of furnace
Suburban..NT, SF etc.
Atwood 7900, 8500 etc.
Brand and model makes it easier to describe what/where----unless you want generic answers. Kinda like "How long a piece of rope?"