I believe those file permissions could include access / ownership rights. That means if you restore the files onto a machine other than from where they came originally then they might have access restricted to users and that don’t exist on the new machine.
Usually there’s a way to take ownership of such orphaned files, but it’s an extra step that not all users will know how (or haves access) to do.
If both computers use a shared method for authentication (i.e. both joined to the same Active Directory domain): yes, restoring permissions will work.
If both computers have a local user account with the same name: probably not. Although both users have the same name, different Security Identifiers (SIDs) are used to populate the Access Control List.
From what I can see, the iCloud user is not used to set the local user. The local users appear to have a UID/GID from 501 (and up if there are multiple users).