Disney are tough, have been for years.
My perspective is post production, and their NDA is one of the strongest around and they enforce it. They also have their security check out companies that work for them. They require internet access to be restricted and even have USB ports on PC's disabled.
But as far as this film goes... I don't think this will hurt them at all.
Either people will want to see a movie about Han's early years or they wont. 'Rogue One' went through a toned down version of this with reshoots and new people brought on to "help" the director and it still made a billion dollars because people wanted to see it.
So do the general public want this? Disney think so. Let's see.