I can confirm this problem in the linux 12.5 catalyst release, no audio over HDMI.
I have this system connected to a receiver and it's important that I get audio over HDMI, I've had to remove the card and hope that it will be supported in a future release. Any updates to this topic are much appreciated.
When you put such a card in your system, you now have TWO potential audio output devices: the one built into your mobo, and the one on the video card. Windows can only use ONE audio system at a time, and it probably was set up with the mobo's chip as the default audio output device.
Go into Control Panel ... Sounds and Audio Devices ... Audio tab, and use the drop-downs to select the default audio devices to be used for sound and MIDI playback and sound recording. For playback, in particular, select the audio system on your ATI video card. THEN use Catalyst to configure the audio playback system as you like. This way, the chip in the video card will feed audio to the HDMI output port on your video card.
I'm not sure if you ever figured out this issue, but I had a similar problem after upgrading to an HIS 7750 fanless, and the problem ended up being that I needed to update the HDMI audio driver. The audio chip on the video card is made by Realtek.
The "ATI HDMI Audio Device" driver on the following page fixed the issue for me.