I remember seeing some spec for the minimum tread depth that they'd sell a used car with - you might be able to find it if you search around here. That being said, they're quite tight lipped about the whole inspection process so it's probably just going to come down to whether your particular SC will actually replace the tires. Seems like a bad idea on their part to sell a car with worn out tires. Possible liability issues. Then again, a lot of their choices these days seem like bad ideas.
Tire condition played a significant part in my recent used purchase experience. Maybe I'll get around to posting a recap of the entire experience (mostly positive), but man sometimes the way these guys do business leaves one scratching their head...
During my delivery appointment (2015 S85 - 28K miles), I was allowed/encouraged to inspect the car prior to signing the paperwork and finalizing the purchase. So far so good! Overall, the car looked great. One of the first items on my inspection checklist was to check the tires (condition, tread, matching, etc). The car had the Primacy MXM4s, and it was obvious in 2 seconds that the rear tires were almost completely worn smooth. Unfortunately, I hadn't had the foresight to bring either a US quarter (4/32" guide) or a US penny (2/32" guide), but even by eyeballing it, the 2 rears were clearly less than the minimum requirement per Tesla's own policy. The fronts weren't great either (ended up being 4/32" on one and 7/32" on the other) but at least they appeared safe.
The tires ended up being my only concern, so I pointed them out the delivery rep (clueless), and she fetched a service adviser who came over to listen to my concern. He said he would take care of it (which I took to mean "yes, anybody with eyes can see those rear tires are as bald as howie mandell") and I went on to finalize the purchase paperwork while he drove the car to the service area of the delivery center to have a technician do whatever.
After the surprisingly brief paperwork process (2 forms), the service adviser returned and informed that indeed the tires are all 4/32", within spec, and that there was nothing he could do as they met the minimum standard. He was obviously lying to my face, but emotion overcame logic and I accepted his response thinking maybe I'm being overly concerned and wanting to get home.
When I arrived back at home, after a brief family celebration, my thoughts wandered back to the tires and I checked them again with a quarter (I don't own a tire tread gauge). Not even close to Washington's noggin -- exactly as I had thought! Over the next few days, I attempted to get some resolution via email with my sales adviser as well as an inside delivery adviser. You can guess how that went, either no response at all, or a vague reply promising a follow-up which never happened. I never even knew the name of the delivery person who conducted my delivery so I didn't even attempt that route.
Finally after a few days of futility, I took the car back to the delivery center in the morning before they got too busy (during my original delivery appointment in the evening, the DC was CHAOS) and explained my case to the delivery supervisor there. Finally! He was in complete agreement and immediately wrote a due bill for 2 replacement tires. He suggested I drive down to the service center (in Costa Mesa they're a block apart from either other) and make an service appointment to have the new tires installed. At the service center (more chaos), I made the appointment and decided to have all 4 tires replaced, 2 per due-bill and 2 at my cost; I selected the OEM Primacy tires. The earliest appointment was 3 weeks away (shocking right?). I lobbied for an earlier time as this should have all been done at time of delivery. Sorry, 3 weeks. I took the appointment. Eventually, through mashing the "edit appointment" button on the App, I was able to get a slot about 10 days out which seemed like small moral victory.
When I arrived for my appointment, the service adviser checked me in and had me wait in the lounge while he checked on availability of the tires. Availability? They literally have a wall completely full of tires. I instantly knew what was coming next. Almost like a bad dream in slow motion, he returned to confirm that they didn't have the Primacy tires (WTH) in stock and did I want the Goodyear Touring instead or yada yada yada. I should have demanded that he propose to me how they would resolve this instead of forcing me to figure it out, but I agreed to just take the alternate tires which ended up being about the same price. Frustration!
Ultimately the tires were installed and life is good but, but it seems that at every turn, where Tesla has a choice to embrace outstanding customer service or to treat their customers like garbage, they choose the latter. I'm most upset about being lied to in person, to my face, by the service supervisor but really there we multiple opportunities for Tesla to show goodwill in this case.
Finally, it turns out when the service center takes in a vehicle for any service, they perform a "courtesy inspection", where they adjust the tire pressure and record the tread depth on the service paperwork. My paperwork showed: Passenger Rear: 1, Driver Rear 1. I don't know if the units are 1/32" or mm, but neither met the minimum. I was more than a little tempted to confront the delivery center service supervisor with this documentation, but I decided to let it drop and enjoy my new used car instead.