I think Hajime declared she was his friend over the journal a while back because she's pushy like that! Her soul does count as "not normal," though. At least part of her soul is embodied in her Note (it was pulled out of her soul) and if it's destroyed, she dies, so that might count. She is pushy, though, like I said, even if she does really care about people, so if that's going to annoy him, she'll just stick to doing happiness drive-bys on his journal sometimes.