If your monitor has speakers and you install the new card's driver, yes. You may have to go to Control Panel/Sound and be sure the default device is set to the card's audio. Modern cards have a built-in sound processor similar to the one on the MB.
It works fine for me. GTX 570 and Samsung 32" HDTV. Just tested it. I can switch between my TV speakers and my 2.1 external speaker system thru Windows Control Panel/Sound.