Probably - No. Once the wheel is tight enough for spokes not to go slack while riding, adding more isn't going to improve things.
Spoke stretch is linear, for each bit of added load, it'll stretch a corresponding bit more. So getting the tension up won't make the spoke stretch any less for the ride induced forces.
Ignoring the influence of hub/rim, wheel (lateral) stiffness is pretty much decided by the total cross section available by your spokes(spoke area x spoke count).