It depends on the app. If the app doesn't support it, then it won't continue to play (like youtube, which shuts off if you sleep the phone).
I assume that's because of the connected standby-mode of the RT, where only the 5th-core of the Tegra3 may be used for playing music, while sending the Pro into sleep/hybrid/whatever it's called today, would stop the app from playing music.My RT Music app and Multimedia8 both run fine with the screen off.