It doesn't have direct references, but it's a setting that's about 50% pirate and 50% vodun/voodoo, and Ron has said it was a major influence.
Monkey Island is definitely a more comedic series, but the less comedic mystical parts (especially in the original SMI) ring similarly to the mystical parts of On Stranger Tides. Like... the Prologue introduces ghosts manipulated by voodoo objects and ceremonies. The first chapters have voodoo talismans used for mundane piracy tasks. It has the heads of a two-headed dog, separated and used as navigational trackers because each head will point to the other. That's a far cry from ordinary root beer that kills ghosts, but it's not a far cry from a rare, unexplainable root that can dissolve spirits. (And maybe the root beer isn't even as far removed, since ordinary candy apparently attracts the ghosts.)
I keep it in my mind when I think of Ron Gilbert's earliest plotting for Monkey Island, in which the Secret was a hidden crevice into hell itself. That hell gate puts me in mind of Stranger Tides' prologue, in which the dead are summoned back into the land of the living through a ceremony.