Uh..
Mind to elaborate?eh? no. that was never stated.
it's stated that it show us up when the Ship is loved by its crew so much.is stated that it also shows up to warn the crew about some damage done, which could have happened apparently cause someone did use the word 'fix' this last chapter.(but don't take this one too serious, we still don't know what happened and after what Wadatsumi did at Totto Land, I'm hesitant to believe)
Regardless of the correction, the Klabautermann isn't really exclusive to 1 ship, so…? You make it seem like the Thousand Sunny is the only ship that is loved by the Straw Hats. Since this legend has been recorded by other individuals, I can assume that's the case.
--- Update From New Post Merge ---
Vivi can totally join for real, "honorary" member or not. All that's needed is for her world to be turned upside down and that's very well what may have happened.
Vivi still has the best chance. Carrot is just not relevant enough to join. At this point Momo or Tama have a better chance of joining than her.
First off, Vivi has already turned down the offer point blank because of her country circumstances. So yeah, while she had a chance, she doesn't now. It wasn't a postponed invitation, she didn't accept it outright because she put her country before her personal desires. So the crew will recognize her as an honorary member. If anything happens, Vivi will always put Alabasta first.
And second, no Momo and Tama don't. Chapter 1 made it very clear children aren't fit to sail the seas. We settled that argument pages ago I believe. Besides, I didn't see Momo and Tama taking out antagonists and considerably helping the whole crew in the face of danger. If anything, they're liabilities, as we see in the current chapter.