From what I can see, the location of your vise inside of a pulled out drawer would not be a very solid surface. I would think you would get much cleaner cuts by having a more rigid surface.
Also, I would move the laptop as metal chips in a keyboard would not be good.
Peter E Actually the bottom of the drawer has been replaced with 3/4 plywood and the sides have been strengthened as well. It will have to do for now. When the weather warms up I will move it to my workshop.