You can go ahead and shoot a bare shaft thru paper, if you just want to drive yourself completely nuts.[8D] Nothing good can come from doing that.

No, a bare shaft without tape will not hit higher. You won't be shooting that bare shaft at any distance far enough for the difference in weight to show up in point of impact. If the bare shaft strikes higher than your fletched shafts, then you need to adjust the nock point up to bring the bare shaft into the group.