Sure. Itachi's saving of Sasuke was a crucial moment in the manga. It was tied to his hidden motives and sacrifices for the greater good of the ninja world and Sasuke's future.
He could also develop through facing new threats in the RWBY world. The Grimm are different from his usual opponents in Naruto. Dealing with them might force him to adapt his combat style and in turn, grow as a character. For instance, he might have to rely more on others' skills in a team - based RWBY battle scenario.
His possessiveness could be seen in his actions towards Sakura. He may be overly protective, like not allowing her to go on dangerous missions alone. He would always want to be the one to accompany her, ensuring her safety at all times. This shows that he doesn't want to share her with any potential threats that could come her way during a mission.
Naruto would adapt to Itachi's life in several ways. Socially, he'd have to get used to Itachi's connections and rivalries. For instance, his relationship with Kisame would be different as Naruto. He might try to influence Kisame in a more positive way. Emotionally, he'd have to deal with Itachi's internal struggles. Itachi had a lot of guilt and secrets, and Naruto would have to either come to terms with them or find a way to resolve them. And in terms of combat, he'd practice Itachi's signature moves over and over to make sure he could use them effectively in battle.
Itachi's personality could become more outwardly friendly. In the ninja world, he had to keep many secrets and be aloof. But in the wizarding world as Harry Potter, he might find it easier to let people in. He may also be more assertive in a different way. Instead of silently following orders like in his past life, he could take the lead in situations, using his own judgment based on his past experiences and newfound magical knowledge.
Maybe in the fanfic, Itachi has done something that goes against Sakura's beliefs or values. For example, he might have made a decision that put her friends in danger.