The Model S will be fine for the ADSS on October 5 (in a parking lot), but won't work well for the for the driving school on the road course track given the profile of driving. Pretty sure there would be range issues at the track, never mind for the drive home. There will also be power limits after 10-15 mins of spirited driving, protecting against overheat. Neither issue fully prevents doing the event or having a good time as long as people are going into it with eyes wide open.
The Model S is really not built for a full track situation (sustained high speed "abuse"), at least in its current configuration. With better cooling, it could work well but it's not a mass market concern so would have to be custom. And then there's the high power charging need.
All that said, the BMW or Audi ADSS events are worthwhile for anyone and easy for the Model S to tolerate. They happen 4-5 times a year (April-October) at Loudon between the different chapters.