No, it's unconstitutional which states: "...To exercise exclusive Legislation in all Cases whatsoever, over such District (not exceeding ten Miles square) as may, by Cession of particular States, and the Acceptance of Congress, become the Seat of the Government of the United States, and to exercise like Authority over all Places purchased by the Consent of the Legislature of the State in which the Same ......"
In other words, the federal government should never be subservient to a state. Granting statehood to DC would place the safety and security of the President and Congress in the hands of whoever is in control of DC if turned into a state.. The founding fathers were specifically concerned about exactly that when they decided that the federal capital would not be located in any state but remain neutral in matters of the states.