If you just want to listen to the songs normally, play it with a microphone only. It will play the song with no miss sounds. Or at least I believe it doesn't. It's too bad you are required to press a button to continue to the next track otherwise, you could basically make a playlist of your songs to listen to through Rock Band 3.
Alternatively go to Practice mode, select a song, then in the practice section menu just stay on "Full Song" and it'll just play the song.