Running fridge Norcold N611 off inverter?

When I had an N611 nocold I believe it was rated for 400 watts@120 volts. That would be a 30 to 40 amp draw from the batteries assuming your inverter is 100% efficient which it isn't. Figure that draw into your total amp hour capacity and you will get an ideas as to how long they will last. I ran mine off of the inverter while going down the road but not while camped. I finally ripped the nocold out and replaced it with a residential unit.

Look up your 120VAC element's Wattage. I think it'll be just short of 300W at 120V. I'm just guessing that with losses on conversion plus the control board, you'll need about 360W at 12VDC, 30-Amps. That makes me think it won't run long on 150-AH. Another guess, I don't major in Boondocking/Solar/Batteries.
What I can say is the industry pretty much phased out three-way fridges because they were energy hogs on 12VDC. They used a lower-wattage 12VDC element for that reason, and all they could do was try to keep an already-cold fridge cool.
Fridge is downright stingy on LPG. How long do you plan to stay out?
We camp a total of probably two months a year. Lots of Stove and Oven, Water Heater in Summer, sometimes Fridge, and I refill about annually. Even then it's not much more than about half gone.