I can't imagine Depp or Verbinski being involved unless they could do things as they saw fit, and I would hope Disney is smart enough to realize the success of the POTC series is because the guys behind it know what they're doing and are best left to do things as they see fit for the storytelling.
I'm not sure if it can be said or not that most of Johnny's films are successful to a fair degree or more so, but there are a number that worked out real well for him. He seems particular about what he does get involved with and if he's game for more POTC, then I'm sure the story will go in a direction he supports or he wouldn't be part of the project. I'm sure some of his choices now are a bit ego too though, what's to stop Disney from having a Jack Sparrow adventure without Depp as Sparrow, it'd be dumb but nothing says they wouldn't, so he may step up too just to protect the character's portrayal and maintain as what he's worked so hard to mold it into, which is nice. It always impressed me that Thomas Jane took a stance on how Frank Castle should be portrayed in Punisher films and opted to not be involved if he couldn't make the character as he saw fit, it's nice to see these guys care about the characters and not just the paychecks.