I've never used fleece as a backing on a quilt but flannel works great. I made a king size quilt for my daughter and used flannel as backing and she says it is so warm and snuggly. I have a lap quilt on my recliner that is backed with flannel and love it.
I love to take 2 layers of fleece and put them together - sew around the edges or cut strips along the edges and tie them - makes a wonderful warm snuggly throw and it is quick.Washes and dries really nicely too.