The momentum of the car is far greater than the rotational momentum of the drive train compoments and engine. In fact, the engine (with your foot off the throttle) will slow down a lot faster than you can slow the car with the brakes.
One variable that is changing is that this added friction is changing your brake bias by effectively adding breaking to the rear wheels. If your car can benefit from more front bias, clutching while braking will help. If it can benefit from more rear bias, it will hurt.
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