Yes, the chair (in their capacity as a member) may object to a unanimous-consent request.

Two months later, the Senate has agreed to this request.

They put Mr. Bean in the chair immediately before him, I guess to make Moore look less bad in comparison.

Another one of those times where I wonder whether a resolution removing a designated speaker pro tempore would qualify as a question of privilege.

It’s always startling when the majority loses a voice vote.