Just to clarify, the website doesn't tell me anything about a confirmed date, but my DS called as soon as the order was confirmed and setup up a tentative appointment for June 24.
I spoke to her today and she still seemed confident in the June 24 date. In order to hit that date, the car would have to go into production by sometime mid next-week (It's a SOCAL delivery which can be is about 6-9 day delivery from start of production).
Woohoo! My Tesla has updated status to "Your Tesla is currently in production". It's possible this thing might get delivered even before the 24th.