Negative, my 2015 Model S w AP1 do not auto-close the charge port. There is not even a motor or anything to close it. It is held closed by a magnet. Opening the charge port consists of the magnet releasing it and letting a spring do the rest.
It also seems that the slightest moisture from the carwash will cause the magnet stick and not release the door to open. Have to tap on it in just the right place while signaling door unlock to get it open in that scenario.