My personally experience is...body makes a huge difference on a car's handling. And I'm not sure if I agree with tuning the car without the body on, because ultimately, you'll be racing with the body on. If bodies don't make a big difference, then I don't think the full size cars and real f1 teams will spend millions of dollars on wind tunnel testing and aero dynamic packages.
Personally I tried running the same suspension setup and tires and just switching the body (for example from a Stratus 2.0 to a Mazda 6) and have notice both a significant difference in feel and lap times. I agree that bodies will not make or break a setup, but it is definitely an important part of the tuning package that must be taken into consideration when setting up your car.
Steve Wang