Yes..that's an excellent question. First: Does the adapter you've mentioned support HDMI audio? Then you have to go into your system preferences on your iMac, then sound, then output, then turn on HDMI speakers. then plug it into your SoundSystem and give it a try !! If not-see if you can find an adapter that supports HDMI audio pass-through...it mentions 1920x1200 video support, but nothing about audio. I'd suggest that if you can find a good deal on a Thunderbolt dock (that supports HDMI audio) and have a spare HDMI cable, then go for it, otherwise try my first suggestion. I think your model of iMac also has Optical out ...yes, apparently it does, but it's a minijack Optical out, and not a standard Toslink or Coax Optical out, which means to connect it to your SoundSystem, you'd need to buy a cable of sufficient length to go from your iMac to that thing. and you'd have to switch the sound to digital out under output -sorry for getting a little technical on you here--- If you hold down the "Option" key and click on the speaker at the top right of your screen, it'll show you all available sound inputs and outputs.
Hope this helps you a bit
John B