If iCloud is enabled, then by default it gets unencrypted copies of these messages from the device unless “advanced data protection” is also enabled which ensures iMessage is encrypted but means losing your password also loses access to these backups. However, disabling iCloud sidesteps this issue and honestly if you want that kind of privacy then disabling iCloud is probably a good idea.
So if one users uses ADP and the other user disables iCloud then the conversion is protected.