I surprised myself and voted 'Yes'.
After looking at the options for a second, and on the verge of instinctively clicking 'No', I stopped and thought about it. I mean, we have had Privateers as a naval unit since G&K, and Civ 4 Colonization did a good job of allowing Privateers to attack without needing a DoW (though much of the rest of Civ 4 Colonization was not-so-good). And we also now have BNW's trade-route system.
So, it seems quite interesting to think of a pirate civ that:
Has a UA allowing it to get double-gold for plundering trade-routes
Has a UU that replaces the privateer and replaces the coastal-raiding free-promo with a boarding promo, gives the unit a promo to heal 50% HP on beating a unit in combat, as well as giving the unit the special ability to plunder trade-routes without declaring war
Has a UU that replaces the musketman with a melee unit called a 'Swashbuckler', which starts with amphibious and embarkation with defense, as well as giving bonus combat strength to the other UU (from the paragraph above) when stacked with it in any water tile.
I mean, this sort of a civ would be plausible. And, because of BNW's focus on trade, I don't see why not, especially since we already have a far more complicated civ -- Venice -- than this sort of one would be. It would be a fun civ, and the city names could come from any CSes that aren't in the game, a la the Hunnic Empire's city-names coming from civs not in the game.