Yes, "toughness" is a technical term that refers to how much a material can yield before it breaks. In that sense, carbon fiber is not considered to be tough at all.
Crash structures that use CF normally depend on it's tendency to shatter violently at failure. If you watch any recent F1 crash that damages the monocoque, you'll see an explosion of debris -- this is by design. Done right, you can use up some of the crash energy as kinetic energy in the debris. Unfortunately, this is extremely difficult to design and test. It's also more or less a one-time use thing, I would worry that day to day bumps and scratches that happen on road vehicles might reduce the effectiveness of the structure.
The undercarriages of F1 cars are a little different, they generally have an aerodynamic undertray protected by a layer of kevlar (or similar material). This is good at reducing damage from occasional contact with the road surface and minor debris, but it depends on the undertray's ability to flex at impact and has to be replaced fairly often.