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Perhaps, but before I tell fully answer that, you must have meet the following requirements, 13 smithing, 13 mining, 13 fletching, 13 invention, 13 crafting, finished all other previous pirate quests, and have done at least 5 clue scrolls.
Speak to the Wise One, who is located on Mos Le'Harmless, to begin.

Don't you do that already though?

I mean its unlucky for someone cause they won't be making it to part 2....
As for the rewards you do get a purple dye (use it to dye any cape dropped from a highway man), half of a pirate ship (top half), a half eaten apple, access to the hidden cove so you can begin becoming the King of Pirates, and most of all, these two pets, who will help you meat the requirements for part 2.