Engraving fabric is different from scoring.  Scoring follows the path of the perimeter of the shape, whereas engraving burns the entire inside of the shape.  

Engraving takes much longer than scoring because the Laser sweeps from left to right and gradually completes the design.

    Engraving works well on fabric that has a pile, such as velvet, velveteen, and corduroy.  Basically any fabric that is fuzzy on top.  The fibers on top can be burned away without disrupting the structure of the fabric.  

    I have engraved printed cotton fabric with fusible on the back for a quilt label. I used a fabric that was manufactured by taking white fabric and printing a solid color and pattern on top.  The color did not saturate to the back side of the fabric so I hoped that the engraving would be lighter than the printed color.  The result was a readable label.