Absolutely, you can use drapery fabric. Why not? The only thing that limits what fabric you can use is your creativity.
Of course, there are things to be aware of. Is this a machine washable fabric or will it have to be dry cleaned every time?
If it is a sheer fabric, you will need to create a foundation to it for stability.
Is it a rough fabric? If so, you might want to use other fabrics as well to make the quilt more touchable. Such as a combination of silk, velvet and upholstery - my mother had a quilt made out of these fabrics when I was a kid, it is still my favorite.