That said, pirates are only truly synonymous with magic in gaming and in modern entertainment cinema (e.g., Pirates of the Caribbean).
Note that Treasure Island (Robert Louis Stevenson), Capatain's Courageous (Victor Fleming), Typee (Herman Melville), and Yankee Ship in Pirate Waters (Rupert Sargent Holland) had plenty of high adventure, with absolutely no FX. There were, of course, numerous legends about mermaids, voudoun priests, and so on... but in the world's most popular pirate fiction, these things only existed as legends.
And, of course, this doesn't touch on the real life exploits of John Paul Jones, Sir Francis Drake, William Kidd, or Henry Morgan - none of which were bolstered by sorcery or fantastic monsters.
There is plenty of precedent for a no FX swashbuckling adventure campaign set on the high seas. Indeed, I'd go so far as to say that there is more precedent for such a campaign than there is for one that includes overt high fantasy elements.