On the 370z, when you turn VDC off, VDC is Off. There is no more traction control, at a minimum, verified by yours truly. You'll still see the orange 'slippage' light come on, but it's just warning you that you're spinning the tires.
I do straightaways with VDC Off. This lets me chirp the tires in 2nd or 3rd (and of course peel out in first), accelerate quickly and show off all speed related things my vehicle can do.
If I plan on hitting a corner at > the posted speed limit, or if it's raining, or if i dont' trust the road or the drivers around me, I turn VDC On. You'll know VDC is working by cornering hard: Your vehicle will hesitate or will be a bit sluggish to respond (talking 1/2 second or so) and when you try to spin the tires your vehicle will lurch, since VDC is removing power from the tires (read the manual for specifics).
Drive with VDC on until you get a feel for the vehicle. Then, slowly start practicing with it off. I took a hard corner on the way to work tuesday morning with VDC off, spun my tires while shifting to 3rd out of the corner and the arse end of my vehicle 'drifted' ~2 feet into the right hand lane. Thankfully, no one was there or i'd be one unhappy camper right now.
g'luck