Not good for Carrot. There are three characters who have joined while being exceptions to this rule; Robin, Franky, and Jinbe. Let’s see if Carrot’s story has any similarities to their’s.
With Franky we knew the Straw Hats were getting a new crew member before we even met him. In Chapter 322 Luffy declared they were going to Water 7 to find a shipwright to join their crew. We didn’t know who it would be but we knew it would be someone. Turns out it was Franky. This became clear in Enies Lobby when he distinguished himself as the only non-SH to fight CP9 1 on 1.
Nico Robin is probably the most unique case to join the crew. She was a mystery throughout the Alabasta Saga and her joining the crew was a shocker to readers and characters alike. Later, Oda dedicated most of the Enies Lobby arc to solidifying her place in the crew.
Jinbe’s joining was a sloooooooow burn. He and Luffy became very close during the events of Marineford, it then took almost half the series for Jinbe to join. Luffy doesn’t even ask him to join until chapter 649 when they literally exchange blood.
So where does this leave Carrot? Unlike with Franky, Luffy hasn’t declared the need to fill a position that Carrot can hold. Unlike with Robin there would be no “surprise factor” with Carrot joining. And unlike with Jinbe there’s no hyper intense bond forged over many years (both in universe time and out).
What does Carrot have going for her? She has the above mentioned quirky/strong traits, she’s sailed on the Straw Hat ship for a long time, and she’s fought along the crew for multiple arcs (two or three depending on how you categorize the action of Zou). It’s totally possible that she joins the crew and becomes a 4th exception to the above. But is it likely? Let’s see if there are any other characters with similar cases to Carrot.
Johnny and Yosaku – They both sailed and fought with the Straw Hats for multiple arcs. Did not get character focus. Did not get offer extended to become Straw Hat.
Vivi – Sailed and fought with Straw Hats for multiple arcs. She got a lot of character focus and developed intense relationship with the crew. They asked her to join, she declined.
Ace – Fought with Straw Hats for a bit. Got lots of character focus. Intense relationship with Luffy. Ace asked Straw Hats to join the Whitebeard crew. They declined. Ace is currently dead.
Bon Clay – Kind of traveled and fought with the Straw Hats (Impel Down). Has gotten some character focus. Developed intense relationship with Luffy. Never asked to join.
Kinemon – Has sailed and fought with the Straw Hats for multiple arcs. Has gotten some character focus, unlikely to join crew.
Gangster Gastino – Sailed with and kind of fought with Straw Hats for multiple arcs. Was hated by the rest of the crew the entire time. Never asked to join.
Pedro – Sailed and fought with the Straw Hats for one arc. Got some character focus. Currently dead.
In this respect, Carrot doesn’t seem special enough to warrant an exception to the rules established above.
So based on all the evidence IT IS VERY UNLIKELY CARROT JOINS THE CREW.
That doesn’t mean it’s impossible, it would just break all story-telling patterns Oda has set up for the past 20 years.
*Theory by Dddddddfried
