Ah yes, the noted historical documentary Pirates of the Caribbean. :)

Premodern alcohol consumption comes up here a bunch. This is an answer about the RN, which may answer some questions for you. I can't speak directly to pirates' alcohol consumption, but I do know that they tended to have fairly strictly enforced codes of conduct, surprisingly enough, and could be punished for drunkenness, implying some artistic licence on the part of the producers.