As said, if a car can produce more force in downforce than its own weight, then at speeds at which it producing this downforce it can be driven on the top of a tunnel.
However, as said, the practicalities of such an experiment make it impossible to actually drive the car. If you could find a way to power an F1 car at the required speeds without it being tethered then it could be done.
TBH, im sure you could prove the concept using a small scale model and a wind tunnel. Making air travel at X speed is much easier than making a car travel at X speed upside down.
Its the same concept as flying. A plane generate enough lift to overcome its weight, and flys. Upside down an F1 car's downforce would be in the oposite direction and therefore be creating lift, and if would be 'flying' in the sence that it would be overcoming the force of gravity.