Can I use a fabric glue to layer my quilt?
Sure, why not. You can glue just about anything. But I don't recommend it. I don't know what size quilt you are talking about glueing but I would imagine you'd go through quite a few bottles of glue . You would have to glue both sides of the quilt to the batting. This would be very time consuming on a large quilt. I have no idea how this would hold up over time, with washing and with general use. I also don't know how soft and flexible it would be. I don't think I've ever heard of this being done.
If you don't want to quilt the piece by hand or machine why not tie it? This will take way less time and work better than glue. Rule of thumb for quilting is to have some stitching every hand span (in other words if you put your hand on the quilt - fingers spread - you should touch some stitching. Tieing a quilt isn't hard - get a curved upholstery needle and thread it with yarn or embroidery floss. Take a small stitch and tie the threads into a square knot. Do this at the center and corners of each block.
Hope this helps,