Coin cell battery for Bluetooth?
No, they won't work. CR cells are designed to deliver maximum a few mA continuously, so a low power microcontroller like an MSP430, for instance running off a 32.768 kHz crystal, may work, but the power for an RF transceiver is much too high.  

The datasheet for this battery even specifies only 0.2 mA as "continuous standard load".

If you would need your RF in short bursts then you could get the power from a large electrolytic capacitor, for say 100 ms, and then recharge it over a longer time, so that the controller still gets enough current. For continuous streaming this won't do.