It turns out that we can do that and it took me so long to "accidentally" figure this out.
1) First, fire up YouTube on your iPhone or iPad and search for the videos that you want to "listen". Then click play.
2) Then click on the HOME button and you will notice that the sound fade out and you will return to the home screen. REMEMBER not to press stop!
At the Home Screen, double click on the HOME button and the multitask bar will appear. Swipe it to your right and you will see media player button and the YouTube icon on the bottom right.
3) Finally click play and the YouTube will continue where you have left and at the same time you can enjoy multitasking to your other apps. Yay!!! This works too with any videos on your video library and wah lah.... Enjoy your "music" on YouTube on the GO!