Does firmware on AirPods get updated when connected to an Apple TV?

I understand that Apple automatically updates the firmware for AirPods while charging when connected to an iPhone. I have some AirPods used only with Apple TV. Will those get updated as well? Or should I occasionally connect the AirPods to my iPhone (and leave charging)? Apple published the page [*About firmware updates for AirPods*](https://support.apple.com/en-us/106340) . That page lists current firmware version numbers. As for updating, it says: > Firmware updates are delivered automatically while your AirPods are charging and in Bluetooth range of your iPhone, iPad, or Mac that's connected to Wi-Fi. That document omits any mention of Apple TV. So I would conclude that Apple TV does not update firmware, but I thought I would ask for confirmation here.