Paper of any type WILL wrinkle. Also, as the coating over top of the paper gets things like small pebbles and even rocks thrown at it, it will make small slits in the coating and the paper will get wet. Be certain to use some epoxy on the surface and let it sit a few weeks before you attempt to glue the paper on, as epoxy will out-gas some. The epoxy will help protect the surface and the paper and subsequent coating will protect the epoxy from UV rays. Note: if you are applying your paper to foam, you won't need epoxy, but there is no telling what will happen when water gets in there.
I put down a kraft paper floor 12 years ago and it is still okay. However, there are small cuts in the polyurethane (12 layers) where drops of water get in just a bit. However, it doesn't hurt the wooden floor, and the water dries quickly. (I would be worried if I hadn't prepared the surface with epoxy first.) Kraft paper is thick, and it still wrinkles, but that was a feature for my floor. Paper will wrinkle more than sheeting or canvas ever would. below is a picture of my floor when it was first applied. You can't see the wrinkles in the photo, but take my word for it, they are there. With anything, you will have to work to remove the wrinkles if you don't want them.
