I would not want the material in a drawer. I like to match and compare fabric when I'm looking for material. If the fabric is in a drawer, I would have to take everything out of the drawer to find what I was looking for.
Have you looked at AlaskaSunshine's tutorial on storing fabric?
http://www.quiltingboard.com/t-43871-1.htm
I folded my fabric the way she did and then I put them on their side in a clear tub sorted by color.