Yes, there's no reason why they shouldn't be allowed. Fanfiction is usually publicly available and as long as they are following the rules of the platforms where it's hosted, they can read it.
They could become more engaged with the overall story universe. Reading fanfiction can make them think about the original story from new angles. Maybe they start to notice things in the original books that they hadn't before. They might also get inspired to write their own fanfiction or share their thoughts about the fanfiction they read with other friends who are also into the Annabeth - related stories.
Well, some of them could be quite critical. They know the original story well, so if the fanfiction doesn't stay true to the essence of the characters or the overall theme, they might not like it. On the other hand, if it's really well - written and adds interesting twists, they could be very into it. They might also compare the fanfiction to their own ideas of how the story should continue or how the characters should interact.
It could expand their imagination. Fanfiction often has unique plotlines that can inspire them to think beyond what they've read in the original books.
In the fanfiction, Percy's interaction with Annabeth's mortal friends could start off a bit rocky. He might be seen as the odd one out, especially if he's just met them. But as time goes on, he could bond with them over shared interests. Maybe they all like the same kind of food or music. And his relationship with Annabeth would play a role too. If Annabeth is really close to these friends, Percy would make an effort to get along with them for her sake, and in the process, form his own unique relationships with them.
When Percy's mortal friends first meet Annabeth in fanfiction, it could be in a busy place like a park or a coffee shop. Percy's friends would likely be struck by Annabeth's beauty and intelligence. However, they would also sense her wariness. Annabeth, on the other hand, would be cautious about revealing too much to these mortals at first. As they start to talk, the friends might ask her about her relationship with Percy, and Annabeth would have to be careful with her answers to protect their world of demigods from being exposed.
They might be a bit in awe at first. She has a certain presence about her that comes from her being a demigod. Maybe they're curious about her and ask Percy a lot of questions about her later.
Well, she might initially seem a bit out of place. Since she's a demigod and used to the world of Camp Half - Blood. But she could quickly adapt and start showing off her intelligence. Maybe she'd impress Percy's mortal friends with her knowledge of architecture and ancient history.
Well, in the fanfiction, Percy might initially seem a bit out of place among Annabeth's mortal friends. He could accidentally do something that reveals his demigod nature, like reacting too quickly to a threat that normal people wouldn't notice. Maybe he'll be super strong when helping them move furniture or something.