They need a warrant to perform any search or seizure—the warrant is the authorization to perform the search or seizure; you can't have one without the other. It isn't "either the search is 'reasonable' or you have a warrant", applying for a warrant is how you document that the search was reasonable in the first place, by providing probable cause supported by oath or affirmation. A blanket authorization for so-called 'reasonable' searches and/or seizures is just another way of issuing an unconstitutionally broad warrant which fails to document the probable cause or to particularly describe the place to be searched or the persons or things to be seized.
However, you are correct that they probably wouldn't have any trouble getting a warrant after his comments. If you make a credible threat, even if your intent was humorous or sarcastic, you shouldn't act surprised when people take you seriously.