I ran Tyvek last year on top of snow. The problem I had last year was everything was slipping and sliding while trying to sleep, and I didn't get enough of it for 3 days straight. I didn't have too much issues with the water though because it was really cold at night. I can see how it could be a problem though if temps were hoving close to or slightly above freezing.
After that, I thought id try a bivy instead, hoping to contain my matt and keep me on top of it while sleeping. Same issue, but heavier item to pack. I am going to what others have suggested, and that is to apply seam seal or something similar to the bottom of my matt. I may also put a few beads on a piece of Tyvek and maybe even the bottom of the bivy and try that. In regards to your question though....I think something below your sleep mat is important because you don't want holes in that. with no inflation on the matt, your stuck with a few nights of sleep on top of hard cold ground and not much insulation IMO.