No, they can't. Only a U.S. Attorney may do that, and often only after obtaining an indictment from a federal grand jury. All they could do is report this to the Postal Inspectors or FBI. But as mo federal crime was committed here so you've nothing to worry on federal charges just for looking in the mailbox. At worse you may have committed a trespass under your state's law, but I can't see any prosecutor wanting to pursue that.
But looking at the law would it be trespass? My mailbox is in front of my house and is actually on a section of my property that has an easement granted to the County for utilities.
§ 21-3. Criminal trespass to real property.
(a) A person commits criminal trespass to real property when he or she:
(1) knowingly and without lawful authority enters or remains within or on a building;
(2) enters upon the land of another, after receiving, prior to the entry, notice from the owner or occupant that the entry is forbidden;
(3) remains upon the land of another, after receiving notice from the owner or occupant to depart;
(3.5) presents false documents or falsely represents his or her identity orally to the owner or occupant of a building or land in order to obtain permission from the owner or occupant to enter or remain in the building or on the land;
(3.7) intentionally removes a notice posted on residential real estate as required by subsection (l) of Section 15-1505.8 of Article XV of the Code of Civil Procedure before the date and time set forth in the notice; or
(4) enters a field used or capable of being used for growing crops, an enclosed area containing livestock, an agricultural building containing livestock, or an orchard in or on a motor vehicle (including an off-road vehicle, motorcycle, moped, or any other powered two-wheel vehicle) after receiving, prior to the entry, notice from the owner or occupant that the entry is forbidden or remains upon or in the area after receiving notice from the owner or occupant to depart.
