No, they don't.No security guard nor Walmart greeter type has authority to search anything....
However, as agents of the company / property owner, they can be given authority to control access to said property, in accordance with the law and company policy. So while a search is "voluntary", should you not want to to be searched, they can deny you access to the property.
I wouldn't think that a recorded message could be considered "oral notification", simply because a recording is a one way form of communication. What happens if you can't hear the recording?
Face to face, IMO, would be the only legitimate form of oral notification, as understanding of the notification can be verified by both parties.