Where are you going to get a broadband connection in the middle of the Indian Ocean if not from a satellite?
Without commenting on the overall feasibility of the idea, you would not need broadband for such a system. Sending a simple message containing data such as flight id, current lat/long, altitude, heading and speed would not need much bandwidth at all. Iridium's "short block data" service is one example of a globally available capability.
It's too simplistic to say that's all you'd need. But the data connectivity itself is not the show-stopper.