Definitely not. You would need the coordinates and weights of all 14 control points to define the untrimmed surface, and you'd need the full detail of the trim curves to know where to stop.
On the other hand, all that detail exists in the CAD file, and it could probably be extracted/dumped without too much trouble.
As someone who has programmed NURBS curves in a non-machining setting, you don't want to even try to convert from NURBS control points to line segments directly by hand. If your controller is NURBS-capable, and if the Gcode command it offers supports the degrees of the surface, you could probably code by hand using that command. I have no idea how you would do trim curves, though, as I have no experience with any NURBS Gcode command. If the command has start/end parameters, I guess you could manually compute where the trim curve(s) intersect with the slice you're about to cut, which might or might not be painful to do by hand. If your controller is not NURBS-capable, you could write a program to take the NURBS data from the CAD file and output line segments. I've done something very similar for generating cross-sections through a NURBS surface for screen display. Perhaps needless to say, it's some industrial-strength applied math.