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For example, if they were driving at top speed through a long tunnel, could they transition to and stay on the ceiling?

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Apparently that is possible.

From http://en.wikipedia.org/wiki/Formula_One_car:

Indycars, for example, produce downforce equal to their weight (that is, a downforce:weight ratio of 1:1) at 190 km/h (118 mph), while an F1 car achieves the same at 125 to 130 km/h (78 to 81 mph), and at 190 km/h (118 mph) the ratio is roughly 2:1.

From http://www.formula1.com/inside_f1/understanding_the_sport/5281.html:

A modern Formula One car is capable of developing 3.5 g lateral cornering force (three and a half times its own weight) thanks to aerodynamic downforce. That means that, theoretically, at high speeds they could drive upside down.

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The applied downforce is there for a reason, to keep it from going airborne (amongst other reasons). You also need it when driving upside down. The fluid dynamics is not really different (assuming constant density). Thus, you need at least $2g$ more down-force than strictly necessary under regular conditions. – Bernhard Jan 11 at 6:59

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