Not sure if you have already completed your purchase, but I did this same thing and bought the car from a private party in DC and drove to Atlanta.
First off - you can't add the car to your account until you send tesla your purchase information and they approve it. This takes 2-3 days (even though their estimate says up to weeks).
This means you can't supercharge it on your account because it's not added. A lot of dealerships I spoke with don't know how to add the Tesla to their own account when they acquire it, and will know nothing about transferring it to you. So bottom line is when you purchase, you'll have to make sure they have the car set up in their app with a card on file, and you can just prepay them $50 or whatever for the estimated SC costs. Then when you get back, send all the paperwork requested from Tesla in (I think bill of sale and your ID) and they will add it to your account.