Guys if you have mean iphone you can. If you have ios 7 all you have to do is open the youtube video with safari, then either go back to your home screen, or open a new tab, then swipe up from the bottom to open the menu, and push the play button. With earlier versions of ios it works the same, except instead of swiping from the bottom, double click the home button to bring up the multitasking bar, swipe to the left, then hit play.
Yeah you can (on iPhone at least) play the music on YouTube and then
Press the home button an double click the home button and press play like you would for normal music
Here's what u do... Play the music for about three seconds and hit the home button. Then lock your iPod / iPhone and hit the home button twice... Hit play
Press the home button an double click the home button and press play like you would for normal music