Quite certainly decent bit rates would be out of question, but would it be possible to pass any information between two computers using this?
Another thing people have experimented with is using the speaker/microphone at above human hearing range. This method usually falls flat because crappy laptop speakers have a hard time going above 20kHz.
One thing I could potentially see working is a laptop with a hard drive generating vibrations with the motor. Then, a smartphone or laptop with an accelerometer could pick up the signal using the coupling through a table.
You generally don't get good enough control over the motors or voice coil in a hard drive to be able to make vibrations like that. I'd probably look at controlling the fans instead to get a similar effect and use the microphone to listen for the noise from them.