For sending a VGA signal even at 640x480 you will need a short h sync pulse of 3.8us at 31.x kHz. You would need an audio interface without filters with single low pulses at 260 kHz samplerate. Otherwise the monitor will just not detect a signal.

You could however use h sync and v sync from the VGA output and feed audio to the rgb channels. But thiswould give a mess of wires and is far from the beautiful idea shown here to just connect the white/yellow plugs differently.