My experience was this - I made my deposit and got the initial flurry of emails, including the one to set up the My Tesla account. Then I waited. I was told 3 to 6 weeks because they were replacing some cosmetic parts (I know the hood was one of them). I started getting a little impatient after two weeks. I would call every few days or send an email. Then, at just shy of 4 weeks, the DS told me that they had all the parts and were going to QC the car. Maybe that Saturday, which would have been exactly four weeks. On Friday, I was told no go. Then early the following week, they said it would likely be that week. Around Wednesday I received the payment instruction email. I reviewed all the paperwork and picked up the car exactly 5 weeks (less one day) after I chose it.
The communication could be a little better coming from Tesla. For instance, telling me what work they are doing on the car and its expected completion date would be nice. When the car was received back from the body shop, that would be another step. As I understand it, they reflash the car. When I tested it, the car was in "Factory Mode". The DS acknowledged that the website could use some improvement for CPO purchasers.
OTOH, this was the smoothest, least stressful, transaction other than my two eBay purchases (both BMWs from distant dealers). And the eBay purchases still required a physical check. The use of an ACH debit is genius for cash transactions. You can send the money the day of pickup and your account shows paid in full. There was no F&I "guy" to sell me undercoating, VIN etching, paint sealant, tire warranties and all the other stuff dealers like to pack on a car. It was very refined experience. Frankly, BMW and the other European makes could take a few notes here.
Part of this may be the no-haggle policy, which removes the "I'll talk to my manager" nonsense out of the equation. I didn't mind hearing the price and being told that there was no negotiation. I was getting a car that sold less than three years prior for over $102K for $56K. I perceived "value". I think that's the issue with other no-haggle style dealerships. The customer still feels like they're getting haggled. If it's not on the new car, it's on the trade. I received a trade estimate from Tesla and they encouraged me to go to CarMax. I did that and the CarMax appraisal was higher, which Tesla honored as its trade value.
If I didn't buy the X5 for my wife just last year, she might be in a Tesla now as well. Although she's still got more range anxiety than I do.
Overall, buying the car was a great experience. The store employees were great and having fun doing their job. And the car really feels like nothing else I've driven. I'm a convert.