Kenn, I think that there is another grounding attachment to the frame separate from the battery connection. Take a look at the frame under the battery compartment, I believe that the green wire is the ground circuit for the 120v side of the converter while the white wire is the battery negative, which is grounded through the converter and an attachment to the frame.
I think you will find that the White wire is actuall 120VAC neutral, IAW ac wiring color codes and the battery negative is eventually connected to the frame thru the converter and the green wire ground. Pulling the battery is likely to have no effect whatsoever on the converter's attachments to anything but the battery... That said, I would pull the battery on general principles -- If it's not there, you can't wreck it!
There are three converter connection schemes that I have seen -- One has the converter completely independent of the 12VDC AND the 120VAC distributions (plugs into convenience outlet and feeds separate fuse panel); one has the 12VDC integral but plugs into convenience outlet and finally, one has both 12VDC AND 120VAC fuses and breakers contained in it -- You have to know what you have in order to isolate it...