With regards to the rating, I doubt the Judge's 'Johanna' would push it up to an NC-17. Burton would have to have Rickman do some seriously nasty self-flagellation s*** to get it that high, and as 'The Da Vinci Code' didn't get an NC-17, I doubt 'Sweeney' would.
However, much as I enjoy being creeped out by the song, and much as I fervently wish they'd included it in the Royal Festival Hall's run, I can totally see why, when you're making cuts, it has to be the first thing to go. Scenes and songs need to advance plot or character. If they bring nothing new, then no matter how amazing they are, they get cut.
What does this song teach us? That the Judge has a thing for Johanna and it's a little bit wrong. You don't need a whole song telling you that though, it's covered entirely by the whole "hi daddy", "hi sweetie; gosh you look nice in that dress", "what's up then, daddy?", "I'm going to marry you, 'kay?", "um, NOT okay!" scene in the middle of Anthony's 'Johanna'.
If this song makes it into the finished film, I'll be VERY surprised.