Yes, there might be some. You can try searching on fanfic websites like FanFiction.net or Archive of Our Own. They usually have a large collection of fan - made stories including ones related to Naruto where Sakura could potentially join the Akatsuki.
One possible scenario is that Sakura could bring her medical skills to the Akatsuki. She might be able to heal some of the members who are constantly in battle and injured. This could change the group's dynamic as they would no longer have to worry as much about their wounds. Also, her combat skills could be enhanced by learning from the Akatsuki's unique fighting styles.
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.
With Naruto, it would be a huge shift. Naruto has always seen Sakura as a friend from Konoha. If she joins Akatsuki, Naruto would be confused and probably try to convince her to come back. Their relationship would become strained as they would be on opposite sides, at least initially. Naruto might see her as a lost friend that he needs to save.
In a 'Sakura and Hinata joins Akatsuki' fanfiction, perhaps they are forced to join. The Akatsuki could be holding something or someone important hostage. Sakura might be trying to find a way to break free from the inside, using her intelligence and combat skills. Hinata, on the other hand, would be more conflicted due to her gentle nature. She might befriend some of the more empathetic Akatsuki members and try to persuade them to change their ways.
In a fanfiction where Sakura Haruno joins the Akatsuki, it could start with her being captured by them. Instead of killing her, they see her potential. She then has to adapt to their way of life. She might learn new jutsu from them. But she would also be constantly torn between her new comrades and her old friends. She could try to find a middle ground, where she can use the Akatsuki's resources to protect both the Akatsuki members who have some good in them and her friends from the Leaf Village.
In a fanfiction where Sakura and Ino join Akatsuki, they might initially be forced into it. Akatsuki could see their potential as valuable assets. Sakura's strength and Ino's intelligence could give Akatsuki an edge. But, Sakura and Ino would not just sit around and follow orders. They would probably start to influence other members. For example, they could make some of the Akatsuki members question their loyalty to the main goals of the group. It would be an interesting dynamic to explore in the fanfiction.
One possible plot could be that Sakura becomes disillusioned with Konoha for some reason. Maybe she discovers some dark secrets or feels betrayed. So, she decides to join the Akatsuki in search of a new purpose. Once there, she has to deal with the other members, some of whom might be suspicious of her motives at first.
In a fanfic where Sakura joins the Akatsuki, there are many possibilities. Her relationships within the group would be complex. She could form an unlikely alliance with Hidan, who is very different from her in terms of beliefs. Maybe she would try to find a way to redeem some of the members. And her joining could also attract the attention of Konoha, which would lead to some tense stand - offs and difficult decisions for both Sakura and the Akatsuki.
Her character could develop a darker side. Being around the Akatsuki, who are often associated with more morally ambiguous actions, might make her question her previous beliefs. She could become more ruthless in combat and decision - making.