Interesting idea. This approach could provide vario data with a higher time resolution than the usual one value per second. But other accustic signals like FLARM warnings can easily interfer with accustic vario detection and the computations involved are not easy, if you want to make them reliable and suitable for a wide range of varios. So i think power consumption is not the right justification for this feature. Another good thing would be, that you can just take your phone into a club glider without any connections whatsoever and also have vario data.

Btw: If you can solder a bluetooth device can be made with less than 15€, so it's quite cheap i think.

1.So frequency of other accustic signal should have specific value and period. I'm not sure how often these signals are in normal flight. I think it is rarely. I prefer to listening vario sounds than other :-) .
2.Bluetooth consumes 20-40mA from phone and 20-40mA from vario device. I think it is really to much for sending data on 1centimeter.
3.If you are buliding variometer you have to put bluetooth device inside for XCS and generating sounds for you.
4.Important with costs: you can buy cheap tablet with micorphone and without bluetooth.

Real-time audio recording with real-time analysis is also a waste of electric power. And it's inherently unreliable and very inaccurate. I believe that implementing this is a waste of developer time.