Assuming this person's bank account includes indicia that he/she also resides in a non-CRS country, will his data go anywhere?
It will go nowhere. CRS is only between CRS signatories.
Example: A Portuguese national lived in Dubai from 2019 till 2021. He was considered a local resident. In 2022 he moves from Dubai to Vietnam (non-CRS) and informs the Emirati bank about his new residency (provides all necessary documents incl. VN tax ID + Vietnam phone number). His bank amends data on record with new residency Vietnam and deletes his Emirati address.
Will he be reported? If yes, where to (Portugal does not seem to be applicable)??
He won't be reported as Viertnam is not CRS member yet.