Should I wait to place ribbon on after the icing dries?
Yes and you may want to go ahead and coat the back of your ribbon in a thin layer of shorteninf first so that the grease from your icing doesn't unevenly darken your ribbon leaving the ribbon looking splotchy.
I have found at times that with certain ribbon fabrics, shortening changes the color of the ribbon, so what I do, is take clear cellophane tape, place it on the underside of the ribbon and trim if necessary, before placing it on the cake.
Or you could use a narrower ribbon just to cover the board perimeter and not the side of the icing. Whatever makes you happier! :)