I think Yamato's joining moment would be her acceptance that she's not Oden...
I don't think that is actually a plot point at all and just a gag which oda probably thinks is funny and all. Her character's main aspect are
1. She was caged in her whole life. Pretty much sheltered.
2. Has dreams to go outside thanks to odens adventure books.
3. Can't travel alone and has pretty much no allies( other than potentially luffy and crew in future)
1 and 2 pretty much suggest her character is setup to go outside for adventure. SHs are the only potential allies she can have at this point for her journey.
But.....I wonder why oda introduced her so late in the story...pretty much makes me think her existence will end at the end of wano arc...some kind of symbolic/illusion thing maybe(maybe adding upto oden gag?)....if not I do think she has very high chances..... though oda has not given us much info as to why she has written her character at all. If its for being a SH then....we need to wait for him to explore her more, give her more of MC(main crew) type qualities/moments....or her arc will be after joining SH. Though as of now...if she just joins and continues without any dedicated chapters to her I would say...its pretty shit. It should atleast be like franky where she sees the SHs fight..has determination to fight for/with them etc.. But honestly writing has been bad and rushed for a long time now....and I wouldn't be surprised if(assuming she is written to be SH) oda just adds her....no different than carrot...well carrot actually seems worse to be since given how little she is actually used given her time in series. But its the same for carrot..oda can just make her join whether its bad or not.