Gameplay shown to the press kinda proved that there will be chases and car fighting, so probably you'll unlock new abilities (handbrake 360, stuff like that) that may enhance your driving abilities as you upgrade the driving skill, but if you don't you'll probably get stuck to a very basic driving level.
Also, they maybe planned a car part system (missions about going to steal some expensive parts for a gang's underground garage in the combat zone?), having to repair your car/ ride, etc... (Or build one with your techie ability), there's plenty stuff to make with a dedicated skill (mostly that there's a Techie role...).
Think about a nomad, mad max style character, he'd have a lot of tech and driving skill (probaly made his own car with diverse parts), able to repair or scavenge parts on other vehicules.
Like V's car in the trailer, we could imagine having a high driving skill would let him be able to have a better control of his car at high speed (in cyberpunk, cars can go up to 300km per hours...), etc...
Lots of stuff to make with the cars, there are plenty rules for them in the original pnp, so I guess it'll play a big role in-game (or they probably would'nt bother hiring experts to design vehicules), I guess we won't even have fast travel, just roads (reason why we will maybe use more a motorcycle than a car in some place), and the driving scenes will be filled with random stuff happening to mess with us, there are fast travel in games like witcher or skyrim or fallout because you're on foot, in a car distances matters less, and it would be part of the charm of the experience, having to drive your adventure throught the shitty part of night city (think about Cowboy's panzerboy job in Hardwired, or Hiro pizza delivery's job in snow crash)