That will work. Be careful about your heat setting. The fusible fleece will not take as high a heat setting as your cotton fabric. I use fusible fleece for most of my art quilts/ wall hangings and it works great, no gummy neeedles, quilts very easily. If your fusible fleece is only fusible on one side then I recommend fusing that side to your backing and then pin basting (or using whatever basting method you prefer) your top to the sandwich.
Rob