A:Answer The short answer is no
When your controller is connected via Bluetooth, audio devices are not supported. To use a headset, connect your controller directly to your PC by using a USB cable or the Xbox Wireless Adapter for Windows or connect your audio device directly to your PC.
if your controller has a 3.5 jack you can connect a wired headset, but if I understand your question correctly and my assumption is that you have a wireless controller that is Bluetooth, then any attachments, such as headsets, are not supported.
Hope this helps