One implication could be that it might strain their friendship a bit. If Adrien really believes this in the context of fanfiction, he might start to act differently around Nino.
One possible reason could be that Marinette has been acting strangely in ways that seem to Adrien to be related to Hawkmoth. Maybe she has been seen in places or at times that are suspicious, like near akuma attacks or where Hawkmoth might be operating from. Another reason could be that someone has been spreading false rumors about Marinette, leading Adrien to believe she has some connection to Hawkmoth.
If Adrien were Hawkmoth in fanfic, it could change the dynamics of the story completely. It might explore his internal conflicts and the impact on his relationships with other characters.
Perhaps Adrien becomes Hawkmoth because he's been pushed to the edge by Ladybug's rejections. As Chat Noir, he's constantly in love with her but feels unappreciated. The pain of this unrequited love could twist his perception of good and evil. He might think that if he were in control as Hawkmoth, he could make Ladybug see him in a different light. He could use the power to create situations where Ladybug has to rely on him more, or at least understand his pain.
Marinette could first be very confused as to why Adrien would think that. Then she would likely be angry. After all, she is actually fighting against Hawkmoth as Ladybug. She would probably start gathering evidence to prove her innocence, like showing Adrien her normal life activities that are completely opposite to what Hawkmoth stands for.
If Adrien becomes Hawkmoth in fanfiction, Paris would be in for a major shock. His friends, like Nino and Alya, would never suspect him at first. And Marinette, who is Ladybug, would be facing a completely different kind of enemy. She's used to fighting Hawkmoth as this unknown figure, but now it's someone she knows so well. It would change the dynamic of their battles entirely.
There's also a great one titled 'Adrien's Duel Against Hawkmoth' on Archive of Our Own. In this, Adrien discovers some new powers that help him in his fight against Hawkmoth. It's really exciting as it shows a different side of Adrien's character and his determination to defeat the villain.
On a personal level for Adrien, he would be straying from his own moral compass. He has always been a character associated with good and helping others. By helping Hawkmoth, he would be going against his own values, which could lead to internal conflict and a possible downward spiral in his character development. He might start to question his own identity and the choices he has made, and it could take a lot of effort to get back on the right track.