to my best knoledge, and I might be mistaken here, DVI is not able to transfer any kind of audio, and the adaptor would not help in this case.
Your only bet would be a real HDMI connector on the mobo which is physicaly able to transmit audio provided the driver supports it.
Again I might be mistaken here, so it might be a good idea to double check before investing in this board.
wrong, both use TMDS. The physical connector has nothing to do with what you can transport over TMDS. You can e.g. have HDCP on DVI, this is no HDMI invention :-)