Sure you can print a poem on the fabric and use it to add to the back. Turn a 1/4 inch edge over on the piece of material (on 2 sides) that will be sewn to the backing. I would hand appliqué the 2 sides onto the background backing fabric and leave the other 2 sides raw edged since they will be on the quilt side and bottom which will go under the binding.
I had to hand appliqué a label on the back of a quilted quilt after I noticed a flaw in the backing fabric.