Side to side it will be as the splines hold it as you would expect. Unless they've changed the casting, which I highly doubt, then it will be loose regardless of how tight the nut is done up as the nut gets to the bottom of the thread on the gearbox before it makes good contact with the new short shift.
Its easy to check from the front of the car, grab the part closest to the front of the car and lift up vertically toward the bonnet, it will move
