I don't think it's as much of a problem as you might think, but you're right that there are some things to keep in mind.
First, like FanaticFringer said, I would always be in the habit of storing the hammock separate from the tarp.
Second, it's going to be a good idea to give anything that was put away wet/damp, a chance to air out & dry as soon as the opportunity comes, what ever you're stowing the wet stuff in (stuff sack, blackbishiop sack, etc).
Even though most snake skins are waterproof silnylon, they aren't "air tight" because they aren't sealed at the ends, so they will allow for a "little" air circulation, but still not enough to justify leaving a wet or even damp hammock or tarp stored in them for any long period.
I started sharing an idea a couple years ago on the hammockcamping yahoo group of making snake skins for the tarp out of netting material so that if a wet tarp was put in an outside, mesh pack pocket, assuming that it didn't continue to rain as a person started hiking that day, a fair amount of the moister in the tarp would be able to evaporate.
Headchange4U did an excellent article about making mesh snake skins for the tarp with an additional idea that he had of adding storage pockets on each end.
http://www.hammockforums.net/forum/s...ead.php?t=1408
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