If the car has the luck to find a rock of more or less his mass, taking the mass and speed into account, can it make a considerable amount of damage in an asteroid?
If marking the "target" with a crater counts as damage, then NASA's Lunar Reconaissance Orbiter has apparently seen what a typical spacecraft can cause.
As many readers know, the Russians sent up a lander aimed at the south polar region of the Moon, but it crashed. Now, the LRO has identified a newly formed crater where the craft likely went down:
The crater measures 10 meters across. Its volume cannot be discerned because the photo does not reveal the precise shape of the bowl, but for a typical "small" crater shape tens if not hundreds of tons of rock must have been displaced. I would not have liked living in a house standing on the site.
The answer to this depends on dozens of variables, such as angles, speeds, and asteroid compositions. We would also have to define "a considerable amount of damage."
However, videos of a comparable sized rock plowing into the moon on Mar 17, 2013 show just how powerful such an impact can be. The video claims that particular impact was equivalent to 5kT of TNT.
I would not want to be either party in such an impact.