I recently finished a "Love Thy Neighbor" pillow that I marked with the Crayola markers.
I had not starched or pre-washed the fabric first. The marker came out of the fabric easily.
It appeared that the embroidery floss then picked up the color and that took a little more
soaking in cold water and even some light scrubbing to get out the last of the marker.
I'd test on a sample first, but you should not have any problems.