actually you might, when you FTP your box have the game in but not active, look around in the files of the game and see if you can find the aaudio section
Some games use simple MP3s and Wavs, but only some.
What I find works very well, is getting one of those microtape 'spy recorders' and just set it next to your tv. You'll get an ultra-high quality recording, especially if you have pets, family, roommates, or noisy neighbors. That adds to the authenticity. lol.
But really, if the FTP thing doesn't work for your PARTICULR title, you can always plug the XBox' audio cables into your pc, and play the track manually through the game's menu.