That depends what amount the producer gets involved. Some just slap their name on it, others get into the grit and see what's going on with the movie.
Also, Chris Nolan and Jonathan Nolan are writing the script. Yeah, I know, the director can rewrite or deviate from the script. But you can't seriously believe that a director is going to have unlimited control when the same person is producing over him and writing the script on the foundation level of the movie. He's pincered. Doesn't mean he won't shitty it up, but unless Nolan gets distracted with the next Batman, I can't see him letting Snyder run wild.