I really don't think it's supposed to be Jack Sparrow. If anything, it's supposed to be reminiscent of the POTC movie franchise logo. Yes, that uses similar imagery to Jack's wardrobe, but I've never heard anybody say that it's supposed to be Jack's skull
Similarly, the talking skull in DL has had those same dangly bits since its 2006 redo, and it has never been claimed to be Jack Sparrow. At the time it was installed, I remember a lot of discussion about how the new look was inspired by the logo; I remember nothing about Jack Sparrow serving as inspiration
Yes, the visual style is clearly influenced by the style of the movies in general, and Jack Sparrow specifically, but I don't think it's literally supposed to be him. If either version were supposed to be him, why don't the voices sound anything like his?