No. Domain Admin certainly is not required, but elevated permissions will need to be delegated. The authentication protocol is not relevant.
More permissions are required to re-join a computer than to join a computer due to there are permissions required to modify the existing computer account object. There are two ways to do this: reset the computer account object, or delegate specific permissions to the objects/containers where the computers exist/will be joined/staged.
Additionally, the computer account dynamic dns record is usually orphaned during this process, so the security principal performing the join would also need permission to change the owner of the DNS A record.