If I were you I would find something to store the hammock and the bag in that will give it some protection from water. After all that's you bed and your insulation for the night. You never know what will happen on the trail and at least you will have a dry bed and bag for the night. Trash bags, stuff sack,etc weigh almost nothing to begin with. Better safe than sorry.
I once slipped while rock hopping across a stream and fell flat on my back with my pack submerged in water. Soaked almost all my gear except for my hammock, sleeping bag, and other assorted items that were in stuff sacks.