If you are talking about using the single composite video cable coming from the video cable which would be the connector with the yellow jack off of the mini-din adapter, then no this is not the optimal connector to use as composite video only supports up to 240i video. 240i means 240 lines of vertical resolution interlaced. Interlaced means per frame only every other vertical line is displayed. Using DVI to HDMI has not only the advantage of being straight digital (vice composite being analog) but DVI has the ability to support up to 1080P of video resolution.
I'm not sure what sjr is talking about with the audio. He's implying that the 9600GT can accept a digital audio feed and combine it into the video output signal. One, I don't think the card can do this. And two even though you're adapting from the DVI ports to an HDMI cable, you can't put audio through the HDMI calbe despite the HDMI cable and interface being able to support audio. This is because the originating interface is DVI which does not support any audio. I could also go on about whether it's even an advantage to have audio running along with video in an HDMI stream.