No, Halo Sport does not have Bluetooth Audio. This is because Halo Sport uses Bluetooth Low Energy; BLE ensures that you get the maximum number of Neuropriming Sessions from your headset before you have to recharge it.
Because BLE uses such low power, it is unable to send/receive large amounts of data in a short period of time (data throughput). Streaming audio requires high throughput, which is only possible with Bluetooth Classic - which uses much more power (up to 100x more).
Note that the Neuropriming function of Halo Sport does connect through bluetooth, so that you can Neuroprime wirelessly.