http://www.youtube.com/watch?v=K2cNqaPSHv0
IIRC some of those GT cars that look like snails compared to F1 cars are "anything goes".
However, here is a truly anything goes car (that has broken the speed barrier on land): http://www.youtube.com/watch?v=LKQ-xj5C2m8
So yeah, an anything goes car will go much faster than an F1 car. But it's going to suck at cornering. We currently don't have anything that can hold such high average speeds as an F1 car can. Not even in any very lightly regulated sport.
For interestingness' sake, modern WRC cars reach speeds of 220kph over gravel.
Top speeds of F1 cars are around 360kph (the Bugatti Veyron can do 430kph), but F1 cares more about cornering speed than top speed.
From Wikipedia:
> The large downforce allows an F1 car to corner at amazing speeds. As an example of the extreme cornering speeds; the Blanchimont and Eau Rouge corners at Spa-Francorchamps are taken flat-out at above 300 km/h (190 mph), whereas the race-spec touring cars can only do so at 150–160 km/h (note that lateral force increases with the square of the speed). A newer and perhaps even more extreme example is the Turn 8 at the Istanbul Park circuit, a 190° relatively tight 4-apex corner, in which the cars maintain speeds between 265 and 285 km/h (165 and 177 mph) (in 2006) and experience between 4.5 g and 5.5 g for 7 seconds—the longest sustained hard cornering in Formula 1.