Can an Apple TV 2 be operated without HDMI plugged in? (This question is related in goal, but not method.)

Shortly after launch, I bought the new Apple TV. A few months later, my girlfriend and I broke up and the HDTV went with her. Apple TV returned to his box, never to be seen or heard from again. I know, terrible!

I've been pondering how I could send tunes to the stereo in my office without running a 20ft cable to my headphones jack, since all the error noises would be pretty disruptive and whatnot. Then I remembered, Apple TV has a Toslink port.

I think that using this, this and this, I should be able to just AirPlay from iTunes. I'm worried, though, that the set-top box might be a bit offended that I don't plan on giving it an HDMI buddy.

Has anyone done this before?
I know for sure Apple TV works fine with AirPlay to send audio out the Toslink (digital optical) with or without a HDMI cable connected.

The converter you linked to seems to take RCA (electric) digital signal and turns it into Toslink (optical) digital signal so I doubt that's exactly what you want to get to a headphone jack with analog stereo (electric) signal.

Since it's not clear what input your stereo wants, it's unclear if everything will work, but the Apple TV will work as you ask.

I have this setup (but Toslink to my speaker) as well as a second stereo connected via bluetooth and a Belkin receiver that connects to the normal 1/8" headphone jack. That might be cheaper than cables and an adapter if the distance is 30 feet or less.