I just finished using cheap copy paper to sew a floral quilting pattern on the quilt I'm working on. I made line drawings of the leaves, vine and flowers, made copies, pinned the copies to the fabric and sewed thru the lines on the paper. I don't know if others have tried it or not. I'm not good enough to do a design like that freehand even though I kept it simple. IMO copy paper is too thick. I spent a lot of time with tweezers getting little bits of it out from under the stitches. It's also thick enough that the stitches seem a little loose once it's removed. I'm hoping it all tightens up when the quilt is done and I wash it before sending it out.
You may not have all the same issues I did if you're piecing but thinner would still be better.
Rodney