I am currently hand quilting a machine pieced top and using a heavy fleece as backing (no batting needed).
Have not gotten very far on it (have done one of the 11" + sashing squares), but am very pleased with the way it is coming out. I'm more or less stitching in the ditch, so the quilting only shows on the fleece side, but re-creates the pattern of the front.
The only thing I would caution you about is that some fleece is more stretchy than others, so be careful when choosing your fleece for the backing.