I still play Driv3r on occasion. Yes it is possible to stunt in it, I've actually jumped from a staircase, bumped a palm tree, then landed the elevated railway in Miami. I'll have to try again and record it.
Anyways, this game looks really good. I actually think the whole Shift feature is good for a game like this. The Driver games are meant to feel like a 70's crime movie with constant action and awesome car chases. I really hope the handling on a Dodge Charger won't be that bad in the full game, it seemed as though it was sliding on ice the entire time.
Almost forgot, any game with a DeLorean = badass. I hope they have a secret one in the game with a Flux Capacitor.