I threw together a quick test for this by using 1 HDMI to my AMP and the other directly to my TV.
So long as the particular piece of software (teamspeak in my case) allows you to choose the output device, then yes, you can indeed have multiple audio outputs.
I was indeed able to hear the test participants over my TV, while music from the Spotify web player was being output on my amplifier. Audio Driver used was the one contained in the Graphics package (9.17.10.2932).
My personal use for this will revolve around Music playing to Zone 2 on my Amplifier.
Phil