Unfortunately USB headsets are not currently supported (for Chromecast play), but it has been mentioned that this will be added "soon".
I'm in the same boat as you, as my best headsets are all self-powered USB headsets.
Keep in mind that even after USB headset support is added you'll likely need to pick up a USB-C to USB-A female adapter, they're inexpensive though.
But I'm talking about a wireless headset. Why would you need an adapter? Or do you mean you need the adapter for that transmitter dongle that comes with the headset?