The idea you propose can be nice. However, the cars or vehicles of everyday traffic circulated on the days before the event but on the days of the race weekend they closed to traffic.
There is a story that I had read some time ago of a driver, I think it was of the Porsche or Alfa Romeo if I remember correctly, who said that at the time in the week before at the event they tried to run in the middle of everyday traffic to try to try understanding and getting to know the circuit better and there was always the risk of being stopped by the police. Sometimes it could happen that in order not to be stopped by the police, the locals helped the drivers with their cars by hiding them in the barns of the farmhouses or in workshops etc.
Then there was always the risk that the police could withdraw his license. Other times, another era.
I was in you the means I would not put them since it is the race weekend.