In a way you could make the point that the argument shouldn't even really be questioning whether Carrot will join. She basically already has unofficially when she joined the WCI group. We don't need to wonder whether Carrot will sail away with the straw hats. Been there, done that. We need to ask, "For what reason would Carrot want to leave?"
She may not be a straw hat, but she IS a part of their adventure. And not just as a friendly island resident, but as an actual travel companion. She literally slotted into the place of a straw hat during her time with them. Carrot's adventure with the straw hats began long ago.
It's as Oden said:
"I simply don't know how to end an adventure once it's begun!" It simply makes no logical sense for Carrot to just decide to leave the crew's adventure when she knows it's only gonna get bigger and better from here.
People bang on about Yamao wanting to sail, but she's a total rando to the crew. They don't know her and have nothing to do with her. She's a fully grown 28 year old and able to lead herself and have her own adventure if need be. Meanwhile Carrot's their actual friend and essentially already a part of their family.
There's no good reason for her to continue her adventure with anyone but the straw hats or to just decide "you know what, I've had enough adventure for today. Back to Zou I go."