Is the tune of the Christmas Carol, “The First Noel” ever used as mourning or funeral background music?

not that i know of

I have no clue. I have always avoided going to funerals, and the two that I was dragged to did not have music. But a good musician can do a lot of tricks with a piece. I knew a church organist who was asked to play something nice while late comers were seated. He played "Get Me To The Church On Time".

Not in my world.