Yes it is a good method, specially if you sing them loud;) No ,doesn't have to be really loud.
If you liked a song check the lyrics and look up the new words to add up to your vocabulary. So you end up enjoying the song, while understanding the lyrics and having learned some new words or expressions.
Notice however that many English songs might include lots of slang and informal expressions, that you can't really use in formal written essays, articles or comprehension. You have to differentiate between both formal and informal language to avoid using any of them in their wrong place.