I suspect that wrapping the pieced front to the back will not match perfectly. The many seam lines will stretch a bit and you will have to make tucks in the pieced part as you sew it down. If you can live with tucks then go ahead.
Look up using facings to bind a quilt. That is where you take strips of fabric that matches the back, sew them around the quilt edge from the front and turn the facing over to the back and hand stitch to the backing.