All searches in the US must be reasonable. There is some variation in what is reasonable depending on circumstances, for example premise searches vs. personal searches; cursory vs. in-depth; emergency or not. It is not more, or less, reasonable to search if the ultimate motivation relates to POTUS vs. a banker vs. a child. As you describe it, the search is by definition unreasonable and is legally forbidden. Therefore, the fruit of such a search would not be admissible in court. Still, the guys in the Secret Service are capable of using intimidation, trickery and illegal force to effect an illegal search. A Section 1983 lawsuit would be possible.
However, walking the public halls in an open building does not constitute a "search" in the relevant legal sense. It is not required that law enforcement locate the building owner and request and receive permission to look in the lobby. The line would be drawn at entering parts of a building that are not open to the public.