Well yes and no to your question. The plane was on their radar so the transponder was working; otherwise they wouldn’t have known what it was, but no, you can’t transpond any data from an airplane’s transponder from the ground.
Time for the pilots and everybody else to break out the cell phones and air phones (assuming phones would work like they did on 9/11 when so many people called from the hijacked planes).
What I was wondering was if the transponder could be set to respond to a "request for information" from the tower, so that the pilot did not have to squawk it manually. I realize that the squawk won't identify friend from foe, but it would give the tower information about the aircraft without requiring pilot cooperation. Done correctly, it could tell the tower much, much more -- including the status of onboard personnel. A certain code entered into the sender could indicate to the tower that the plane is in a silent "alarm" mode, for example.
I'm no aeronautical electronics wiz, but it seems to me that a microprocessor could be programmed to respond with some minimal datastream if prompted by a poll from the ground on a certain frequency.