No it isn't correct. I suspect Jason misread the question. "Man the boats" is fine. "THE man the boats" doesn't make sense. You don't use an article before a verb.

It is correct. In this context "man" is verb that means something like, "take control of, or be responsible for, or go to the boats and sail them." Sailors have a special language. You could also use "man" this way, "can you man this booth while I go to my car? Just answer any questions people have" or "John, I need you to man the front counter while the receptionist is on her lunch."