I also have the Apple A/V component cable. It will not mirror your iPod or Safari if that's what your after. It will play YouTube videos or Netflix movies on your TV or any app that supports Video Out but does not mirror what's on you iPod home screen or any other than apps that support video out.
iTunes movies, Netflix movies, YouTube, those type apps support video out and can be played to your TV but it doesn't mirror your iPod's home screen or Safari if that's what you were thinking. Just apps that support video out. I also have non-jailbroke (4th gen) iPod Touch.
When you go to play a movie and have the cables to your TV the iPod screen will be totally black and have a message saying "This Video Is Playing Through The TV" If you disconnect the cables then the videos/movies play on the iPod.