No, Tom. In Roger Abrahams's Deep the Water, Shallow the Shore it's clear that the island whalers do sing when rowing after whale. They might sight it from a great distance and the chanteying was very useful. But you're also right and they would go silent where they got closer.
I love "Paddy Doyle." I wish there were dozens more known verses but there are only a few more than given -- Who stole poor Paddy Doyle's boots? and We'll drink 'er up and be gone