Yes, the cars are available in as many colours as are available in the dealer when you look at the car. If it comes up with a race livery, there's usually only 1 colour choice. There are a few exceptions, such as the Honda S2000 LM race car which you can buy in 3 colours.
You'll win Bentley Speed 8 for the Sarthe II 24hr race, and yes, it will be British Racing Green, exactly as the Le Mans car was, in tribute to the famous green "Blower" Bentleys of the late 1920's. Why would you want a Le Mans Bentley in any other colour?