It would have probable safely landed at Teterboro.
How would the automated system recognise that it had encountered an emergency situation and not just a system degradation? There is no definition of what an emergency is so how could you program that into the system? The most likely scenario is that the automated pilot would have tried to restart the engines but kept flying in a straight line as it would be programmed to do. By the time it got to the point of EGPWS warnings it would be game over. I think the humans in the flight deck demonstrated their value