I don't think it'd work in the configuration set out like that, no.
We don't have composite like that, so not entirely sure what the colours mean.
I'm guessing the Red/White leads are for left and right speakers, and the two yellow ones are input and output in video.
Right, well if you wanted TV output for video (not sure if you do), the composite video ports will have to be availble on your graphics card for a TV out.
For the sound, since theres 2 stereo ports (Left and right), you'll need a Y stereo jack that will add those two ports into one stereo port to go into the sound card in the Line Out.
One of these will do:
Make sure, that when you buy one like this, the end that goes into the sound card has two black stripes around it. You'll see on the picture of what I mean.
If it only has 1, its a mono output.
So after getting one of those, you'll attach the left and right ports from the composite cable, and place it into the Y Stereo Jack.
You'll then place that into the Line Out of the sound card, and then attach the composite cables to the TV the standard way.
I believe that would then work
IF YOU JUST WANTED SOUND OUTPUT TO TV AND NO VIDEO:
If you just wanted that, then I'm sure there are cheaper alternatives, than to get a full video/audio composite cable, and leaving the video outputs to go to waste, but its one way of doing it.
If your TV had a Line In input though, the process of just doing this would be alot simpler, but I've never seen a TV with one