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It now seems to be a standard practice to aero-mod drag cars.
I have seen several drag cars that completely delete the grill opening for better aerodynamics.
They would have no other reason than aerodynamics, since - if anything- the engine would need more air not less.
Also, I have seen several cars that extend the trunk out for better aero.
Rather than just have a huge spoiler at the back like a NASCAR racer, these cars actually extend the trunk out a good foot or two to manage the airflow better.
I don't have a picture handy, but there is a 10 second Supra with this sort of deck lid extention.

So... yes aero mods would help.

I have to wonder how much though, since even a drastic reduction in drag would only be beneficial for the few seconds that the car is running down the track - but then ... in a sport that places the winner by 1000ths of a second, anything helps !