Yeah, if Neko beats Peros then Carrot is done. In that scenario, I would assume the purpose of this whole avenging Pedro arc was to teach Carrot that she still had a lot to learn before going out into the world just like Wanda tried to warn her. I guess she would grow from the loss and return to Zou to train kind of like the Strawhats in the time skip before joining as an ally in the end. I think there's still a chance she gets a real fight with Peros though. Neko might lose but weaken him enough that Carrot can finish him, or he might have to do something more important and leave her to finish the fight. Either way, she 100% has to defeat Peros to join the crew. This is her only relevance to the plot, and she has not been set up at all to do anything else in onigashima. It's looking slim, but I still have hope.