Impossible to answer, with out naming specific states. Some states require sales tax to be paid at time of purchase, regardless of where the car is registered/home state of the buyer. In all cases I know of, the only way to get out of paying the tax to the pruchasing state is to have the car delivered to you out of the purchasing state. Usually a well-documented paper trail is required (trucking bills of lading, etc).
Other states only charge the sales tax at time of registration. Out of state buyers who are registering the car in their home state do not pay sales tax to the dealer's home state.
Specific states I am familiar with:
First group (paid at purchase) - MA, CA
Second group (paid at registration) - VT
I've bought cars in MA, brought in CT plates, and driven home. Paid 5% to MA, and then 3% to CT (CT sales tax was 8%, but they grant a credit for sales tax paid at purchase).
I bought a car in VT and registered in NH. No sales tax, period. Several VT dealers near the NH and MA state lines routinely advertise "pay no extra tax to VT - out of state buyers are exempt from VT tax"
But Tesla can/should deliver the car to your home, and there's no such thing as a low-priced out of state dealer, so this should all be moot, right?