I don't think that's an effective way.
First, the lyrics are too short. That means a person needs to listen to so many songs. And usually the topics in songs are limited.
Second, some words' pronounciations are changed based on the song's rythems and the singer's accent. Unless accents learning are needed, it's quite easy to learn inaccurate accents.
Third, learning English via English songs has the risk of over-reliance. People are easy to notice the catchy tunes and ignore the lyrics. And sometimes "learning English via English songs" can be an excuse of avoiding learning English.