Whether or not God invented the speaking tube to call to his disciples is immaterial; was it in use on 19th c. sailing ships? Not just one ship, but in sufficient use for it to be known generally to crews?
Hugill and others speak of 'blowers' (see above) keeping the crew in line with blows- true, sometimes, on Black Ball, but does this have anything to do with 'blow the man down' in the chantey?
Terry, in his book, speaks of the chantey as one used with the halyards, and is satisfied with 'blow the man down' as equivalent to raising the top sails, giving no further explanation.

A couple of verses to give this post a salty flavor:

We went over the Bar on the thirteenth of May.
To me way-ay, blow the man down.
The Galloper jumped, and the gale came away.
Oh gimmie some time to blow the man down.

So we'll blow the man up, and we'll blow the man down.
Way-ay, blow the man down -
And we'll blow him away into Liverpool town.
Oh gimmie some time to blow the man down.

Now is that the sails talking?

Composed but not copyright by an unknown chantey man, the line coming into his head because the wind was blowing and the crew could make sail.
See Richard Runciman Terry, 1921, The Shanty Book, J. Curwin, London. (On line, Gutenberg)