Yes, the Model S has a 12V battery. There is no direct connection from the shore power (charge port) to the 12V battery. It's charged from the high voltage LiIon drive battery from time to time. This is the power architecture of the Model S...
Charge Port -> On-board charger -> High voltage LiIon drive battery -> DC-DC converter -> 12V battery.
The 12V battery provides power to the on-board electronics (3G/LTE, WiFi, Keyfob Radios, CPUs, ...) when the main pack contactors are open. This is known generally as "vampire load" and there are numerous threads on TMC about that. The 12V battery provides the power to close those contactors when the car turns on or when the 12V needs to be recharged. This power architecture is part of the safety features. If the car is ever in a crash, first responders can simply sever the 12V loop in the frunk to force the contactors open and thus isolate the high voltage inside the main drive battery, to eliminate the wiring in the car from being energized with potential dangerous high voltage.