A self-driving car is probably a better thing to compare to. And in that case, most people would probably argue that it's behavior would be deterministic, even if it could learn in some capacity.
Although, after making that point, is there really a difference between a self driving car and a car and a driver in your example? Probably not. They're both being driven by something, and the answer shouldn't change based on what the driver is.
Although, after making that point, is there really a difference between a self driving car and a car and a driver in your example? Probably not. They're both being driven by something, and the answer shouldn't change based on what the driver is.