LED as Zener: is this a good way to lower the BOM cost?
Yes, however you should bypass the LED with a capacitor such as 100uF electrolytic and you should expect the LED to vary in brightness a bit with the sound output. 

You may not be able to get full sound power output while keeping the LED within maximum current specifications. 

You could put a diode (eg. 1N4148) in series and use an emitter follower (eg. SS8050) to avoid both problems. 

Or use a TL431 which costs less than CNY 50 per K in Shenzhen.