No, actually he cannot adjourn Congress. He can call Congress into special session, but the president has no right to address the legislative branch directly. All of which said, who cares? I have long believed the whole SOTU thing was a political circus and we need to go back to sending it up in writing. Trump should one up Pelosi and refuse to address congress... ever.
I guess I read this wrong.
SECTION 3
He shall from time to time give to the Congress Information on the State of the Union, and recommend to their Consideration such Measures as he shall judge necessary and expedient; he may, on extraordinary Occasions, convene both Houses, or either of them, and in Case of Disagreement between them, with Respect to the Time of Adjournment, he may adjourn them to such Time as he shall think proper; he shall receive Ambassadors and other public Ministers; he shall take Care that the Laws be faithfully executed, and shall Commission all the Officers of the United States.
The President can adjourn Congress if the House and Senate disagree on whether to adjourn.