I used fleece as the backing and fold over binding on a flannel quilt for a grandbaby. It turned out really cute & snuggly. I haven't tried it for a shaggy quilt but I don't why it wouldn't work. Prewash the flannel first in hot water and a hot dryer and I would used 2-3 squares of flannel so it's really fuzzy.
Around here, folks are taking 2 contrasting pieces of fleece and putting them back to back then fringe cutting all 4 sides and knotting one piece to the other with the fringe. It looks good when they use very highly contrasting fleece.