I agree with Scott because there is an AMAZING variety of weather-resistant ply out there that would last as long as you need it. Undercoating comes in for those folks like me who get ten miles from home and wonder if they left the stove on. It's just a little added insurance against rot but mostly peace of mind for me. And with camping, that's what I'm after...a clear, peaceful mind.
Having messed around with old cars for so long, undercoating became to me a necessity for a few reasons: 1) anti-corrosion 2) anti-vibration 3) anti-noise 4) some limited insulation value.
With a tear you can possible need it for #1, depending on your type of wood.
You can
definitely get a benefit from #2. Nobody likes fasteners that vibrate loose--again, not probable, but
possible. I know that an undercoated car feels more solid than an
UN-undercoated car.
#3 wasn't so obvious to me until I realized that the majority of sound coming from my laptop's speakers (which are in the BOTTOM of the thing!) reached my ears by bouncing off whatever surface the laptop was sitting on. Scenario: You're trying to get to sleep in the state park campground and your "good" neighbor has the stereo up too loud. The music hits you through your walls AND bounces off the ground to come through the floor. Don't believe it? Ever put your ear to the ground to see if the posse was a-comin'?
Of course, I hope you're not concerned with road noise in the tear...riding in there is probably NOT a good idea!
#4 is dubious, but every little bit of thickness underneath on a cold morning sure couldn't hurt.
One factor which I didn't think of (because here in the South we don't have to) is road salt corrosion on the metal pieces (frame, axle, road box, etc.). After reviewing back through Arne's post, I realized that might be something he (and others) deal with. OK, I'm SURE they have to deal with it. I'd think too that road salt stuck to your plywood wouldn't be too attractive either, and the undercoating would give you a nice barrier all the way around.
Another reason to think about the salt (do they salt the roads in Kansas?) is because you might just get a wild hair to travel to a salty state some cold winter month. I've been known to do crazier things. One less thing to ever, ever, ever worry about (translation--no intrusion on the teardrop state of mind).
Don't sweat it though...build the tear and see how you like it without undercoating. You can always upgrade to it anytime.
Peace.
Undercoat, you're supposed to undercoat.
