To quote the potential showstopper first:
It has an effective Strength score of 2 (so it can lift 20 pounds or drag 100 pounds). It can trigger traps and such, but it can exert only 20 pounds of force, which is not enough to activate certain pressure plates and other devices.
While today's sailboats work with all kinds of tech that may make this possible, in the Age of Sail (which is more modern than most D&D settings) this would not fly. 20 pounds of pressure is nothing. That's not enough to lift a lazy cat up, it's surely not enough to be a deckhand.
That said, yes, all tasks for a deckhand are "simple", but if you needed to command each and every one of them (like with a crew of landlubbers) the commanding officer would be hard pressed to actually get any sailing done. While that's not so bad with humans, because they learn, you cannot sustain that with a "force" that only follows orders and never learns. This is what the "Profession: Sailor" is about: knowing what simple tasks to combine to follow an order without the captain explaining every pull and push of every rope in detail.
So even on this grounds, the answer would be no, because
It can’t perform any task that requires a skill check with a DC higher than 10 or that requires a check using a skill that can’t be used untrained.
However, having ships crewed by magic is cool. And you are free to research mightier versions of the unseen servant, either as player or DM. For a cool ship you will want Permanency anyway, so maybe you can find "Mordenkainens pretty much improved servant" somewhere, if you look hard and ask your DM nicely.
I'm sure products have done this already. Probably with lots of handwaving the rules, but it's your game. If you think it's cool, go for it. A necromancer should be able to raise the dead to do it, unseen servants of around that spell level should be able to do it, too. After all, such a ship is more of a story thing and not really unbalancing anything.