Carrot has zero chances of joining the Strawhats, her character is rabbit poop. For all the characters who have been on the front scene, Carrot is the worst character in the entire series in that regard. She's the archetype of a filler character, she's not needed in the story, remove her and nothing changes.
If she were to join the Grand fleet, in term of character development she had be under Bartolomeo, Cavendish, Sai, Hajrudin and even Leo, that's just how terribly bad Carrot's character is.
And the fan made Perospero plot point make no sense at all, it's non existent, Pedro blew himself up of his own accord, her anger isn't justified or if any it should be directed at Big Mom. They invaded a Yonko territory, people put their life on the line, people die, like Wanda said '' it's not a game Carrot ''. Her whole character is so out of place and silly.
Again Carrot is complete and utter dog shit.