yep, your furnace has no need of the trailer being plugged into shore power.
it runs off the 12v battery. the only thing that you'll need shore power for is the a/c, the 110v outlets, the 110v AC side of your fridge and recharging the battery.
did someone tell you that you needed to do this, to run the furnace?
and Zoe the Wonder Dog(R.I.P.)
'07 Roo 23SS pushing an '07 Chevy Avalanche
Equalizer WDH and Prodigy BC