I think it takes a bit more than a self-referential aspect, or of addressing the audience directly, or references to other non-fictional persons, to ‘break the fourth wall’ with a song.
The problem is, most songs don’t have a ‘fourth wall’ to begin with.
With dramas on stage, TV, or in the movies, there’s an implicit pretense on the part of performers and audience alike that what’s happening on stage/screen/tube is real. When we watch, we suspend disbelief and mentally enter into the world being created there. Being self-referential, or interacting with the audience, or the leading actor making references to his real-world ex-wife, break this pretense.
It’s that pretense that is the real ‘fourth wall,’ and a performer singing a song rarely brings that pretense into being to begin with. The singer sings songs, and some of them may be stories that you can enter into, but you don’t lose sight of the singer, and the singer only briefly forgets about you, too.
I’m not sure what it would take to create, then break, the ‘fourth wall’ in this context. The closest I’ve experienced to it is on the studio version of Neil Young’s “Powderfinger,” when near the end of the second verse, he sings:
And I’ve just turned twenty-two, I was wondering what to do
And you (or at least I; YMMV) half expect Neil, in the persona of his fictional protagonist, to step out and ask you for suggestions.