Not to rain on your parade but I highly doubt this. By all accounts, VINs aren't assigned till the car is out or almost done with assembly. And since you're in Los Angeles, the travel time is only a day or two. I wouldn't expect a VIN to be assigned to you till you're a week or less out from delivery. The June 16-30th is essentially SA speak for "hopefully by the end of this quarter". And with Tesla already saying internally they reached Q2 order capacity almost 2 weeks ago, I would say even by June 30th may be a stretch.
But hey...we're all pretty much in the dark here so who knows. <shrug>