I was reading through this a bit and found this
Hey guys, I have been having this same problem, and I finally got it fixed. I have no idea if the so called fix was from what I did intentionally, but hopefully it was and helps you.
I was going through random settings on my receiver (an Onkyo TX-SR605, oldie but goodie) and I saw in an HDMI setting that there was an audio out, which was defaulted on. I turned this option OFF. I assume this is basically passing the audio connection from the video card (mine's an EVGA GTX570) through the receiver to the HDMI out (in my case a projector with no audio capabilities). For my receiver, I found this in Menu > Hardware Setup > HDMI. I assume this will be different for most receivers though...
I had also read another forum post from 2011 about a guy who had a problem with the NVIDIA audio device not showing up in Windows sound playback devices only when his projector was turned on, but it DID show up when the projector was off. So I was trying different things out and the projector was turned off when I did that other settings change. So basically I had my projector off, but my receiver on, and I had switched the HDMI output for my receiver to NOT output audio, and then the NVIDIA device/my receiver showed up as "plugged in" in the playback devices. After that, I turned on my projector again, which screwed with the playback devices for a sec, so I did have to restart my iTunes, but it did work right after that. I hope this helps!
I'm using an EVGA GTX 570, mini HDMI to HDMI cable, a 50ft HDMI cable, Onkyo receiver, and an HD Panasonic projector, which I don't remember the model name of. Thankfully I don't have to use a second card or anything and I am able to get audio through with an extended desktops setup.