Yes, I also believe she's meant to find moments to stand out while on the crew. However, if she's on the ship, it can't just be as an unofficial tagalong anymore. When Nami joined, despite all the developments that only happened later, she was still considered part of the crew. Same with Usopp, same with Robin. And if Carrot is on the ship with the intention of staying on it and Luffy accepts that, that in itself earns her the right to be called a crewmate.