Correct, if there are multiple audio streams you can choose which one you want to hear although the first one will most likely be the default when starting playback. WMP has very little to do with Media Player Classic. So I don't know where the option is for WMP, but I expect that there is an option to switch audio stream.

Here's the site I found which had a post referencing the "AVI-Mux GUI" I mentioned earlier:
Dual or Multi Audio AVI with subtitles (MPEG4 XviD DivX) - VideoHelp.com

I had been all over "Vegas AVI: Render > AVI > Custom > Audio" before as well and found nothing. I think the only thing you can do with the Multi-Channels option is Stereo/Mono/Surround settings.

Maybe it's something a newer Vegas might have? I have Vegas 6 which I know is starting to get fairly old.

Also, I just found a small guide on doom9 which shows how to do this with nandub:
Doom9.net - The Definitive DVD Backup Resource