I'm surprised others with a 34G haven't responded.....yet. I have a 2020 31UL with the Whirlpool; here's my input FWIW: Yes, the fridge runs on 120 vac. It comes from the inverter. Love the thing; it makes ice cubes as I roll down the road and it has never caused a problem of any kind. Others have had troubles .... mainly related to the fridge startup/cycling back on .... and after reading on this forum for the past year, it seems to me that it usually involves a different brand res fridge and the inverter (or their batteries,perhaps) just aren't up to the task. I hope your experience is as good as mine; I suspect it will be.
Your furnace operates on 12 vdc. Just know that the blower motor draws considerable current. If you are parked overnight and running the furnace, your OEM coach batteries will definitely want charged the next morning; maybe before if the fridge is on much at night. At least that has been my experience.
Hopefully others will chime in. Good times and safe travels to ya.
Ed Sievers in Denver
2007 WBGO Outlook 31C SOLD
2020 Precept 31UL
Toad: 2016 Kia Soul w/6-spd DIY
"Be the person you needed when you were younger"