One possible plot could be that Sakura joins the Akatsuki in an attempt to spy on them for Konoha. She might pretend to be a rogue ninja interested in their goals. However, as she spends time with them, she starts to understand their motives which are not as black - and - white as she initially thought.
In a fanfiction scenario where Sakura joins the Akatsuki, it could be that she is disillusioned with Konoha for some reason. Maybe she feels that Konoha has been using her or not treating her fairly. So she decides to join the Akatsuki as a way to find a new purpose. Once there, she could start to influence the group's actions in unexpected ways. For example, she might try to persuade some members to use their powers for more positive or at least less destructive ends. The Akatsuki members would have different reactions to her. Some might see her as a valuable asset, while others might see her as a threat to their long - held beliefs and goals.
Well, in a fanfiction where Sakura joins the Akatsuki, she could bring in her medical skills. Maybe the Akatsuki has some members with serious injuries or ailments. Her presence could cause internal conflicts within the group. Some members might trust her immediately because of her skills, while others might be suspicious of her motives from the start.