What is your goal in trying this? Do you not want the look of binding, or do you not like the work of it?
The biggest problem I see with your plan is that the backing won't be well attached to the front and batting. If you attach a hanging sleeve to the backing, the quilt could sag and slump in unpredictable ways.
Other people have suggested facing, and folding the backing to the front as binding. I would probably go with a combination of the two, if your front is large enough: Cut the backing and batting about 2" smaller than the front, centre it so that the front sticks out by 1" on all sides, and quilt it. Then bind by folding the excess from the front to the back and stitching down. It will give you a nice, seamless look on the front, and save the work of a facing.