The Tesla website at Model S | Tesla Motors states: "When approaching a Supercharger station, Model S automatically parks in an open stall." That means that the car will have to know, for every possible Supercharger stall, if the charging pedestal location requires nose in or nose out parking. Some Supercharger sites offer both! That means the car needs not only incredibly detailed information about each site and stall, but also has to know its own location extremely precisely. If Tesla can make that work reliably, I will be impressed.
If I may be douchebaggy enough to quote myself while also patting myself on that back (think of me dressed in one of the Dumb & Dumber tuxedos while I do this:
I would not be surprised if this was the whole idea behind why they wanted to do the autopilot in the first place. Cars charging and queuing themselves is the most efficient use of charging infrastructure. There is nothing worse than coming up to a supercharger and finding someone that's been there for 4 hours. The problem are the legacy cars. They are going to slow everyone else down.
Unfortunately I bet it will be difficult ( from a legal point of view ) to have an unoccupied car that is waiting to supercharge autonomously pull into a stall when it becomes open. But *that* would be awesome. If you could just leave your car near the supercharger and it would eventually charge when it can.... wow. Maybe it will be easier because the superchargers are on private property - and not on public roads. Maybe your empty car can drive around legally in a private parking lot. Still scared of it running over a tiny pedestrian though.
Tesla has never, to my knowledge, defined what is meant by "private" wrt the self-parking. Personally, I think it means at your house. Some seem to think it means at a mall parking lot, because that is private property. I think Tesla means a place where there are no pedestrians or moving vehicles...
I think Elon has actually talked about AutoPilot enabling autonomy in parking lots because the car can maneuver slowly enough that it can use the sensors to move safely. Private property would be "not on the highway", anywhere that normal traffic law does not apply.
The Supercharger charging cables require a human to connect them to thecart. That isn't going to change anytime soon.