I don't think this is the case. Lithium batteries are generally much better with deep discharge than lead acid. Trying to power a heavy load below a certain threshold voltage will quickly and permanently damage them, but generally there is a low discharge disconnect that kicks in before this point. I don't presume he'll notice any particular ill effect.

Like nkurz said, the battery management circuitry will usually disconnect the battery before it discharges enough to damage the electrolyte. Granted, this depends on the circuitry in question (i.e. your $0.05 battery controller chip from Shenzen may not do this), but I would hope that Tesla is actually investing in proper battery management circuitry.

Given that the car won't let you discharge below 20% margin, it probably isn't affected at all.