Simple answer: no.
Slightly less simple answer. The Youtube app would have to be coded in such a way that allows it to output audio in the background (like most music player apps). Google would never allow such a thing because using Youtube to listen to music kind of goes against the intended purpose: watching videos.
not entirely accurate - download an app called Stick It - and it will let you play videos as well as youtube in a floating window
Simple answer: no.
Slightly less simple answer. The Youtube app would have to be coded in such a way that allows it to output audio in the background (like most music player apps). Google would never allow such a thing because using Youtube to listen to music kind of goes against the intended purpose: watching videos.