I don't do all over quilting, like pantograph in long-arm quilting, but I do quilt separate designs on my borders. Even though you are going to cover the edges with the binding -- and therefore catch the threads of the seams -- I would do the same with hand quilting because of the risk of losing stitches before you get the binding sewn on. Run your stitches near the edge and then turn another direction while continuing stitching. Bury the knots as usual.
Jan in VA