I have used fleece as a backing and spray basted and it was fine.
I only did straight line quilting, though, and I used a walking foot. I didn't have any problems this way. Also, fleece is stretchier one way . So, I used the less stretchy top to bottom with the greater stretch going across since the majority of my quilting lines were vertical.
I have used fleece as a batting and them FMQ with no problem. Or you can straight line quilt. I use spray basting and didn't have any issues.