Is it possible to design the cars to actually make the wake clean? Like put the airflow back together at the rear of the car? I know that there are rules that limit sizes and shapes, I am just more interested of aero-neutrality is even possible.
This doesn't answer your question, but it reminded me of F1's Overtaking Working Group and what they are looking at relates to your question a bit (diffuser and rear wing in particular).
If you ask it at a given distance behind the car then yes at the certain distance it is possible.
If you ask from 1 meter behind the car no, that's not possible, slipstreaming is based on turbulence.
And turbulence is dependent on the pressure gradient over the object (the leading car).
As soon as you have a car that produces lift/downforce it is almost impossible to have laminar flow behind it.
Hence even if possible, the slipstreaming wouldn't be possible anymore.
However nowadays F1 cars use the coupling of diffuser and rear wing to enhance the rear wing.
This condition help the boundary layer to stay attached on the rear wing but as the particles leave the wing they slow down very fast because of mixing with the diffuser wake, so they leave into turbulence, a very turbulent one.
So yes in 2009 the diffuser will be moved and rear wing higher so that coupling will be less important.