She's as much of a Strawhat as Momo, Kinnemon and O-Tama. All given invites, none will ever go anywhere
If she ever goes to sea it's as the captain of the Neo Beast Pirates, you think Ulti and Page One joined her for no reason? Or do you really think Ulti and Page One join the Strawhats?
The Beast Pirates rallying around Yamato is going to lead to them becoming her Scabbards, and defending the country in her absence. I could see Ulti and Page One following her as her direct subordinates, like Neko and Inu did with Oden.
Even in the recent cover story Carrots seems to wave good-bye XD
It's funny, because almost all of my theories regarding Wano characters going to Elbaph has Momo flying them there in Dragon form. I think the Kuja + Rayleigh and Shakky, the Revs, Morgans + Vivi, and Shanks will show up in Elbaph soon. But, this theory was for Teach taking over Wano.
Now, I think V. Nusjuro and the WG will arrive via Abyss to take over the country, which is much worse for Wano, since Teach wants the territory and loved Oden, and the WG despises Wano and wants to eliminate them for making the Poneglyphs and being Joy Boy's allies.
Boa clearly wants to see Luffy, and the Kuja need to flee Amazon Lily because the WG can attack it easily, and all Kuja, even the non-pirates, are labelled as Pirates by the WG (even the kids).
Momo is looking at Carrot and Boa as they fall: I think Carrot could join with the Kuja to sail to Elbaph. The Kuja stopping at Wano before heading to Elbaph makes sense, they would resupply/rest/form an Alliance with Wano, since Wano is a Straw Hat allied nation.
Carrot would be allowed on the ship, because she's a woman. If Gloriosa IS Yamato's mother, I'd imagine Gloriosa would want to get dropped off in Wano, too, to see her kid.
Carrot and Boa are both reaching out towards Luffy: we'll see them soon. Kinemon is also looking in Carrot's direction; it's possible she was ordered to flee.
It's also possible Momo orders Zunesha to head to Elbaph, but, Zunesha is a large ally for them: I can see Boa letting off a lot of the Kuja in Wano, then taking the remaining forces to find Luffy in Elbaph. Makes a ton of sense for the Kuja to officially ally with the Straw Hats, now, they're coming to the New World.