Larry,
You are correct, it appears your model Dometic does not require DC power to operate on gas mode. The units that require DC power to run on propane seem to be the ones with auto ignite. Should the flame blow out the control box would sense the loss of flame and activate the igniter, relighting the burner. I see your unit (RM2333) manual does not show or indicate the presence of an auto igniter. I assume you do not have a control box attached to the back, bottom left side of your unit.
You may have to remove the refrigerator in order to clean the flue though.
I did find this pdf manual for your unit:
http://bryantrv.com/docs2/docs/operating/rm2333.pdf There is a section dealing with cleaning the flue and a drawing of the flue baffle.
Dick