You are asking if the Model S has a limited slip differential, ie, a differential that mechanically limits the percentage of drive torque that can be sent to the wheel with lower traction.
The answer is no, it does not. It has an "open" differential (like your 1992 Mercedes). In a situation like you describe, the Model S differential will also route all of the torque from the motor to the wheel without traction.
But that's not the whole story, as someone mentioned above. The Model S (like many if not all cars these days) has an electronic system that uses the brakes to mitigate this problem. When you get into a situation where one wheel is spinning substantially faster than the other, the electronics will apply the brake on the faster-spinning wheel. The resistance provided by the brake pads mimics the resistance provided by traction from the tire, and effectively causes the differential to route power back to the "unstuck" wheel.
This works reasonably well. The downside is that the extra friction from the brake application reduces brake life, though in non-track driving it's not that big an issue.