I've used fleece as backing before. No batting was used but you could if you want. Also I thought about using a wash away stabilizer but didn't.
My QAYG wasn't done block by block, but rather section by section. I was making a lap quilt so I divided it into 4ths so there'd be fewer seams on the back.
There is a definite bump at the seams but not too bad since I kept the folded over edges narrow. After I straight stitched two of the sections together I then folded all edges (blocks and fleece) to the inside and used a decorative top stitch to hold it.
I hope that makes sense.