Quest wise, it perfectly ties into The Chains that Bind. You'll go to Delphos, Nova Aquila, Achaea and Knossos in that order, so just do it alongside then. Reward wise, it's strange they don't even give you a trial, like a 1 day version, or a permanent but normal/average speed version. In Wizard, you can buy a few permanent ones, like the Blue Dragon - but sadly excluding various giveaways/events, your only chance of a free permanent mount (that's actually a speed boost) in Pirate is PVP rewards or farming endgame bosses like Kane or Bran the Raven Lord. The mount is only worth 500 gold, not sure the Vultures would be satisfied with that.
I did not know that Bran could drop a mount. Yeah it`s super disappointing going through all that effort and not being able to get the mount anyways. They really need to include some mounts that can be alternately bought for gold just like Wiz. I really don`t mind spending 100,000 for a house in Pirate and I didn`t have a problem spending 90,000 gold for the Bengal Tiger or the Proud Lion mount. Also if you had the patience you could get free mounts from fishing or from crafting to which Pirate has neither.