I don’t like this idea as a standalone civ, but it could definitely work as a revolution. Haiti is already essentially a pirate themed revolution. Ideally, Haiti would be based more on the slave revolt and have units such as Maroons, but apparently it’s too racist to actually depict the history of oppressed black people so they get to be pirates.
Haiti already has Buccaneers as a variant of the Pirate. However, it should be its own class of outlaw, especially after Pirates have been changed into shock infantry.
More units like the Freebooter you mentioned could take it to the next level. There could be even more revolution options like Jamacia, the Republic of Pirates, or Libertatia. These could even be secret revolutions only available to players who age up with the Gentleman Pirate.