NO! You do NOT have to have an inverter to use an 18cf electric refrigerator.
The inverter is in the front of the 5th wheel, it has both 12V and 120V coming into it, and with the switch on the front of it, you decide which source you want it from. I worked in the power industry for over 4o years, and if you DON'T open your doors a refrigerator or freezer will stay cold up to 36 hours. So, in an RV I would say a few hours would be OK. With your gas/electric you have now, you will have a A/C plug for it to plug into, so you can just plug it into it. The amperage is about the same, so there is no worry there.
Hope this helps God bless!
Mike and Judy
Wherever we are parked is our home
2009 - 36RD5S
2007 - Dodge 3500 6.7 Cummins
May God bless