It'll work if your TV has HDMI with seperate video, via DVI to HDMI cable/adapter. If you plug into a standard HDMI it will look for video and audio and make your speakers buzz. You need a dedicated HDMI for video only and there will be a red and white port for the audio.
Other option is to get a 8800GT that has s/pdif built in so you can send audio with the video via DVI to HDMI.
To get full 1080p thats the only 2 ways you can do it unless your TV does 1080p VGA which I havent seen so far.