Okay, so the interesting thing here is that the Nao doesn't look like she'll be an actual romantic rival. Instead, she seems to be a way to reveal the Honjouji's self-sabotaging, self-defeating nature. She just barely has this idea bout tousling the lead's hair. Then she meets the new girl who goes ahead and does it and she thinks "Oh, so that's how it is. Never mind then." Like she doesn't have a chanc e. Remember what Takuya is like. He's barely got any sort of romantic interest in anyone, so it's unlikely he's hung up on this childhood friend. But Honjouji just assumes he is. At the first possible moment, she assumes her sudden romantic leanings are for naught.
So, Nao probably isn't Honjouji's enemy. Because Honjouji already has an enemy and it's Honjouji.