I don't think so. Granted, he is clearly standing next to what appears to be a Tesla Model X, at the Hawthorne Supercharger Station, but I don't exactly think this means he's the first person to own a Model X.
Not that he wouldn't be a good choice; this 6502-jockey was, if you ask me, the cooler of the two Apple-founding Steves, and would certainly be a good candidate for such an honor. But I think that's a factory prototype.
We've seen these sleek prototypes before, and the lack of license plates does sort of suggest this is a prototype.
Still, Woz does say "our" new Tesla. Maybe he means "our" as in "humanity's?" Maybe they did give Woz a pre-production one; if so, good for him. That big rear cargo area and frunk should be nice and filled with Nixie tubes and circuit boards in a week.