Reading the exact notes of a song on sheet music can help you to identify all of the correct notes in a fast run or something like that, if those notes are all annotated on the music.
If you're going off-base on a melody somewhere, musical notation will show you exactly what note was written for each step of the way.
That said, that's a lot of work to go through unless you need that. If you can sing or play an instrument "by ear" then it's a lot more expedient to just listen and then sing it exactly like you just heard it. If you are good at discerning pitch, this is the way to go.