I had a similar expreriance............ except mine did have the under cover on it. Bought my first "learning camper" 2 years ago. Nice little 24" Skamper, been shedded all its life, the underside looked like it had just come off the show room floor!!! Went camping one weekend, the back end was pointed towards some timber fifty feet away, dog (black lab) slept under the camper each night.
Guess What??? Damn Pack rat climbed the stablizer arm and chewed through that nice clean undercovering and then through the insulation untill he hit plywood. I about freaked!!
About all I could do is pack it all back up there and sprayed some of that spray foam insulation around. Sawed the excess foam off and then put black 100 mph tape over it.
Thank goodness it didnt get any wires ect.
Flash forward to my "new" camper
Went camping, same lake area......... wooded area.......... see where I'm going with this??
Got about a mile from the lake returning home from a nice weekend.
New 2010 Ford pickup, only 5,000 miles on it.
Yellow Check engine light suddenly comes on
Stop and look around under the hood then decide there wasn't much else to do but drive the 30 miles home.
Get back to work next day and bring home the scanner box.
Knock Sensor bad
Finnally find the sensor, down under the intake manifold DEEP!
Guy at work is a Ford mechanic, he gets the part and only charges me $100 bucks to tear the intake off and put the knock sensor in.
Yeah, I got way off from the topic?question a little.........
Long story short, I would definatly put the under belly back, just one more layer to protect the "soft underside" of your camper. jdadoug