The suddenness of the transition is going to matter more than the actual angle in most cases. Often the road drops towards the curbs, compounding the problem of a driveway that goes up. Here in CA, some roads have deep rain gutters that usually make things worse by lowering the car an inch or two just before the sidewalk. In many jurisdictions (at least in CA), only city/county approved contractors can do sidewalk work, which includes the driveway ramp in typical designs. While they can probably make a shallower transition for you, these contractors typically charge top dollar (law of supply and demand). I've seen driveways with a pipe laid in the road gutter and covered with asphalt. That eases the transition while letter water drain by. I have no idea how legal that is in your neighborhood.
From what I've seen of the Model S, the rear end is higher and slopes up as it moves away from the wheels. The front end, however, is not only low, it's low the whole length. My guess is you'll scrape on the front before you scrape on the back. For comparison purposes, the Roadster's specs show it has a greater ground clearance than the Model S, and most Roadster owners have scraped the bottom. Heck, if you pick your car up at the Menlo Park assembly plant, you'll probably scrape bottom (at the front) as soon as your wheels hit public pavement for the very first time!
If you're able to enter/exit your driveway at an angle, that will help quite a bit. But, that's not always practical.
