Well sort of.
They can't tell writers what they can do, but they can tell them when they're doing something contradicts something else, and they're consultants on the canon. The story group, or at least Pablo tries to explain things that might not be clear in the side materials, like the Visual Dictionaries for the movies.
Some writers listen more than others. Like from what I hear, the Rogue One, Solo and TLJ writers embraced the Story group more than JJ Abrams did. The novel and comic writers as well.
Apparently Abrams definitely doesn't like to be told what to do to the point that SW animated writers were not telling him things specifically so he wouldn't go out of his way to contradict it.