I think the answer depends on the type of paper and also on the quantity and consistency of icing piped on top. Frosting sheets are thicker than wafer paper and stick to cookies quite well, so piping on them isn't a problem. However, wafer paper, in my experience, is more prone to lifting in areas where it gets too damp, especially along cookie edges. So, if you are over-piping relatively sparingly or with a thick-ish icing, the underlying wafer paper is unlikely to be affected. But if the icing piped on top is loose (i.e., wetter) or a lot, the moisture can cause the paper to buckle and lift off the cookie. I've most often had this happen when piping beadwork (loose icing) along the edges of wafer paper. As an aside, I also find that icing clings less well to papers (of both kinds) than to icing, and so decorations more easily pop off papers over time.