Has that ever been done? I can imagine it'd just skip out of the gears and crash horribly. You know, like square wheels. Fitting warmed-up soft slicks and doing it on an F1 track or specialized tarmac would probably yield better results.
You actually want / need some tire flex to absorb the initial torque. This is especially true with electric motors, where 100% of the torque shows up instantly (gas engines have a torque curve)
Watch a NHRA funny car start in slow motion. The big fat back tires actually wrinkle up into themselves a lot, then spring back out[1].
The Drive Unit in the Model S was designed by Borg Warner and looks roughly similar to this cutaway of the Roadster's gearset: http://www.sae.org/dlymagazineimages/web/516/7953_8579.png
The issue is in the straight gear-to-gear interface where ~600NM of torque is transferred through a contact area measured in square centimeters. Modern metallurgy can produce some very strong alloys but any flaw means the gear teeth will wear at an incredible rate, leading to the widespread reports of noisy/failed Drive Units. I'd imagine that future designs will use a planetary gearset which spreads the force over more teeth/surface area, that type of gearset would look like this: http://www.rohloff.de/uploads/pics/planeten_start.en.jpg
[1] http://books.google.com/books?id=GPNKAAAAMAAJ&lpg=PA87&ots=m...