Can we pair our AirPods Gen2 to the Apple TV 4K?

Yes...it fact it might already be working.

If you are tvOS 11 or newer and your Apple TV is logged into the same iCloud account as your iPhone or iPad that has already been paired with your AirPods then it should just work. AirPods automatically pair with all your other Apple devices that are using the same iCloud account.

But, if this does not work for you, you can pair them manually by...

1. Put your AirPods in their case and open the lid
2. Hold the pairing button until the light on the case starts to flash white
3. On the Apple TV, go to Settings > Remotes and Devices > Bluetooth and select your AirPods from the list.

Once you pair your AirPods, much like you would an iPad or iPhone, you will need to connect to them when you want to use them. One way (and there may be others) is to hold down the Play button on the Apple TV remote when you are on the Apple TV home screen and choose the device you want to use for playback.