What you are hearing
The disc turns air into a tone: every slot that passes the nozzle is one puff, so the pitch is slots times turns per second. That tone is the carrier. The valve makes it louder and softer in step with the message, here an old melody played by a pure tone.
In the air, the melody is not there as notes. Its energy sits in copies on either side of the carrier, at the carrier frequency plus and minus each note. Listen to the siren and you will hear a buzz that swells and fades; the tune survives only as the rhythm of the swelling.
A detector gets the tune back by doing two crude things: it lets the air push only one way, then smooths away the buzz. That is how a crystal set hears AM radio. Here it is done in software: rectify, then low-pass filter.
So, would it work?
As amplitude modulation, yes: put the right detector at the far end and the tune comes back, buzzing a little. Hackaday's verdict was that you would mostly hear a 10 kHz buzz, and without a detector that is about right. Set the disc to 120 slots at 80 turns a second (9.6 kHz) and listen to the siren.
What this page does not model is everything that makes it hard in brass and water: how far a horn throws a 10 kHz whistle, wind, echoes, keeping the disc's speed steady, and what the detector would be made of. It is a demonstration of the signal, not of the machine.