No. The ride's 'story' is complete nonsense and Jack's place in it is inexplicable.
1. "Dead men tell no tales." And yet, they're going to tell a tale. And the two people on the mist don't really introduce themselves. So... who are they?
2. Beach with pirate and mermaid skeletons. OK... why?
3. Living skeleton piloting a sailing ship in the rain. OK... why?
4. Ship attacking a fort. British ship? Pirate ship? Not clear. Looking for Jack Sparrow and gold. Why?
5. Pirates (?) torturing townsfolk looking for Jack Sparrow. They all seem to want to protect him. Is he their local hero? Oh, look, someone's watching from around the corner and hiding. Is that Jack? Well, since he's willing to let people get tortured to protect him, I guess he's no hero.
6. A slave-bride auction. I hear the Redhead is preferred. What does this have to do with the tale?
7. Several pairs of figures are on a laughable fast roundtable that is supposed to simulate running I guess. Is this based on a cartoon show? One pair is carrying a chest... of treasure? Is that part of the tale? Are any of the other runners part of the tale? One oaf is looking at a treasure map bragging that Captain Jack Sparrow will never get his hands on it. And look, I guess that's Jack popping up from the barrel reading over his shoulder.
8. An alcoholic pirate talking to his cats.
9. A sea shanty that carousing pirates sing while a city burns. A pirates life for me!
10. Pirates in prison trying to call over a dog who inexplicably holds the key. A pirate's life for me, indeed!
11. Captain Jack with his hoard mumbling something incomprehensible. Yay (?) Captain Jack! (?) He... did it?
This 'attraction' exists purely based on the power of nostalgia.