Yes, if you could find them. However, single transport ship shouldn't clear out half of Caribbean while sitting in a port.
That post was an answer to another post, which has disappeared. I can't remember the post exactly, but it was along the lines of not wanting pirates as modifiers (or special mechanics), because then it would still be possible to have a pirate infestation, even though you have a fleet big enough to destroy the pirates. I actually wanted to emphasize, that you had to find them first too.
And I was promoting the idea of the trade lanes themselves being infested with pirates and the ships sent to control that lane also fighting pirates. This part would be especially good for gameplay, because then it would still be necessary to assign ships to trade lanes even if you control all the land around the cot, i.e. Spain still has to protect it's trade colonial trade from English privateers, even though it controls the whole trade lane home.
Although come to think of it this might be a problem around heavily contested trade lanes, such as the Mediterranean ones, because all the ships vying for control would effectively wipe out all the pirates, which definitely wasn't the case (this was also a problem with the old system).