Yep, I've been doing it this way for years. I saw Judy Niemeyer demonstrate this technique on Simply Quilts. Except she and I use freezer paper for paper piecing so only the top sheet that has the pattern lines is copy paper. Like Kathy said above, I staple the layers together to make the number of "copies" I want.
Because I want to preserve the paint on the antique treadle machine that I use for this process, I put a quilted sandwich under the paper stack so that the staples have no chance of marring my beautiful machine's surface. Since there is no thread it simply causes lots of holes in that quilt sandwich after hundreds of uses! A side benefit of using the quilt sandwich on the bottom is that I have more control and stay on the lines better than without it. I think the cloth is grabbed/moved by the feed dogs better than the freezer paper.
Finally, I use my rotary cutter and a ruler to cut on the borders of my pattern. I love this method since I don't want to put freezer paper through my copier.