Having finally ordered the soundtrack it turns out you were partly right!

From the composer's comments:
"...The piece was written early during the production period so that the Hogwarts school choir could be filmed singing it, but due to the inevitable chanegs that take place during the making of such a large-scale film the sequence was omitted..."
"...If you listen to the middle chanting section you will find that it appears in nearly all the significant Dumbledore sequences..."