Can you connect the new wireless headset to a laptop? Or do you need an adapter?
If it is a jack connection, it should work.
Bluetooth would be better but the Microsoft dongle which also controls the gamepads (Wi-Fi connection)
But then you don't need to buy wireless headphones
So is it necessary or is it possible without it?
If you have bluetooth on your PC, it is not absolutely necessary, but I would really recommend it to you, the latencies are much lower