Does the HDMI on the Gen 4 Apple TV support audio return?

Yes you can Airplay audio to HomePods from settings

1. Or: Play the audio that you want to stream from your Apple TV, then press and hold Apple TV App/Home  to bring up Control Center. 
2. Select Airplay .
3. Select your HomePods

Or Swipe down on the screen to select Audio

https://support.apple.com/en-us/HT202809

Note: if you’ve updated your Apple TV to tvOS 13, the TV audio will also remain on and you cannot use the ATV Remote to adjust the volume. Deselect the TV (to Off) to be able to use the remote for HomePods - if you wish.

To directly address your question, there is no Audio Return Channel feature on the Apple TV box. Video and audio get send from the Apple TV box over HDMI, but no stream gets send to the Apple TV box over HDMI.

the instructions were to send send audio from your apple TV set box to HomePod. Check out the link I posted to see how this works.

You cannot airplay from a device to Apple TV then send that to HomePod in a three way set up

your Apple TV set box is connected via HDMI to the TV. Once that is set up this way you can airplay any app running on Apple TV to the HomePod (Netflix, Prime, Movies, Music App etc)

You can’t connect HDMI directly into a HomePod being there are no ports on HomePods. You can’t just use your tv to airplay to HomePod either.. as in cable TV.

I hope I understood you correctly and you understood my answer!

Or someone else might provide a better answer.