nygal, everybody has their own idea on this subject, my personal way of doing it is to remove the paper and pin pin pin and pin some more. When I started paper piecing about 14 years ago I left the paper on but found that my machines feed dogs didn't like the paper and it wouldn't feed through my machine evenly, also a pain in the petootie to try and pin through paper and fabric without it moving, plus it was a hassle to remove the paper from the seam allowances. So I started to gently remove the paper then join my sections.
I don't remove my papers until I am ready to sew it all together. Hope this helps