It wont do anything. Neural "overtraining" isn't movement specific, it's systemic. Westside prevents neural accommodation by rotating the exercises but in all honesty they are not really at risk of neural "overtraining" since they only do 6 max efforts lift per week (3 lifts above 92% for bench variation, 3 lifts above 92% on squat/dead variation).
In the layer system the volume of neurally demanding work is much greater both during a session and during the week (4 sessions vs. 2 with Westside).
Basically changing the exercise every week with the layer system will not work. Neither for preventing neural fatigue nor to give you results (it WILL make the system less effective).
I've been doing this for 20 years and have trained using pretty much all possible styles of training, including Westside. If rotating the main exercise worked on the layer system to prevent neural fatigue don't you think I already would have recommended it?