Tbh, with the way you've described the character, she sounds like she'd be a garbage fake claim. You make her sound just completely irrelevant and irrelevant characters are more likely to be town so it can throw townies off that not every single important character is gonna be in the game. Case in point, in JoJo, Shinobu–Hayato's mom–was a town role even though she didn't do squat in part 4, while Hayato himself a very pivotal character to the defeat of Kira was a fake claim.
If it were up to me, I'd add Fuji's character in the game and definitely would not make her a fake claim. Flower's an experienced host so she knows how fake claims work and AL as the coach for sure knows how they work. I find it hard to believe that if Fuji's character is as meh as you make it out to be, she'd be a fake claim.