I wish I had seen this earlier.
Yes, you can get an S in auto. It's a sportshift style with paddles on the steering wheel for manual mode. You cannot get the actual JCW full package in auto but you can certainly get a LOT of the components added on as extras.
I have not driven a turbo S with an auto but I know the Supercharged S can be made quite spunky with a pulley upgrade. I don't think its an awful tranny but I wouldn't own one. Also, be very aware of your warranty. You do not want to know what the S sportshift auto or regular MINI CVT costs to replace.