I stitch around the edges of a top if it has lots or pieces in it. That anchors the stitches in the edge pieces so that they don't come apart while quilting.
Binding - after trimming the quilted quilt, I just put the binding on. No special stitching to hold the sandwich together are needed. However, in the case of tying or very loose quilting, it might be a good idea to do what you suggest.