No. My girlfriend and I are 140 hours in and still not finished, and I'm amazed at how smooth the coop works with the story. You can each be different places doing different things, or you can travel together, you can each have your own relationships with npcs. A lot of conversations with npcs will repeat depending on who's talking, but important story ones won't. As long as you mostly stick together and make choices together, you'll have every option a single player game does.