Does carrot join the Strawhats?
She is an ally of the Straw Hat Pirates during the Four Emperors Saga, mainly during the Whole Cake Island Arc, where she joined the Sanji Retrieval Team to rescue Sanji on Whole Cake Island and continued on with the crew to Wano Country.
Does carrot become part of the crew?
One of the Musketeers of Inuarashi who also trained under Pedro, Carrot is a rabbit Mink who has traveled quite a lot with the Straw Hat Pirates already. She became a part of the crew when Luffy set off for Whole Cake Island and has been with them ever since.