I dunno Judy, I would think the non-skid back would be slightly heavy; actually with the backing and the rug, it might be a tad cumbersome. I don't know how the needle would react to the backing "fabric" eitherl.
Maybe embroidering a border and/or creating an embroidered binding and then sewing those on. I would trust a sewing machine with the backing before I would trust my embroidery machine. Just me.
Joan/NJ