I have a 2000 S2K (AP1). There is one spot on the car where road turbulence picks up rocks and creates lots of scratches (rear driver quarter panel). If I put side skirt extensions on the car, will those reduce that problem (by changing the aerodynamics)?
Might reduce it.
Might move it somewhere else. Might be worse. Hard to forecast unless you can find someone with an identical car who has done it. Or and extremely skilled aerodynamic flow modeller. 
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if you consider how much a rock or a pebble weighs and how much surface area it has, also the amount of force required to get the initial trajectory to change… just like most things people bolt onto their road-going vehicles, this has almost nothing to do with aerodynamics.(if you were really motivated you could probably alter the location of bug splats, though.)
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Excellent point that should have been obvious to me.
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My two cents: The skirts aren’t going to do anything unless they physically block rocks from bouncing up. Air is going to try pretty hard to stay attached to the side of the car.
If it’s the spot just ahead of the rear wheel, you could put a decal or rock guard right there, you see that on 911s fairly often.
If you want to do a full aero kit you could try to get the end plates on the front splitter to throw off vortices and clean up the flow coming off the wheels. I dunno if that would help with rocks but you would have cool race car aerodynamics.
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Think it would be far easier and cost efficient to just put some sort of protector there like the clear plastic film (think its called PPF). That is unless you want the look of skirts as well.
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My knowledge about the aero on S2000 has little to do with reality and much more to do with driving dynamics and laptimes 
There are a lot of #trackdaybros and #Hardparkers that run side splitters, but I’d be remiss to think that I knew the real benefits of them. Physically blocking the rocks seems to be the right call IMO.
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