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you say yes but do we know that as a fact?
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Yes. we know this as a fact. Scientists much smarter than you or I have done the tests and the math. No matter where you put a turbine in the airstream around a vehicle the net energy is a loss and seven less efficient than using your stock alternator Even a stationary windmill is very inefficient the only way it works is because it is harvesting energy that's generated by the sun. The wind around your car first has to be generated by the car at a very low efficiency. You can't get it back unless its going to be lost to braking anyway. Even then. it's still a net loss.
I know it seems like a flat plate would have the highest drag but your plywood reference is not correct. A turbine has drag orders of magnitude higher than the flat surface of it's blades. That's what the chart I posted shows. There isn't really a wind shadow effect of the magnitude you are hoping for. Aerodynamics is a tricky mistress.
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Vortex generators are old tech. My new and improved vortex alternators are unstoppable.
"It’s easy to explain how rockets work but explaining the aerodynamics of a wing takes a rocket scientist.