Thinking about the SOTU debate, I knew the Constitution mentioned it. Here is the text from Article II, 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 bolded section got me curious. POTUS can convene them regardless of what Nan says or wants. I found this opinion from 1989. Here is the final paragraph. The opinion details it out.
Tl;dr: POTUS can give SOTU address officially and formally is he so chooses, imo.
Notice who it is written by.
Moreover, to contend the President lacks the power to convene when Congress is in session but adjourned is to contend that the President may not during time of war, for example, summon Congress to Washington if Congress chooses to remain absent. Such a contention would also allow Congress, by remaining formally in session but adjourned for most o f the time, to defeat the President’s constitutional power to convene Congress.
In sum, the Senate has been convened many times and for many rea sons. It has considered both nominations and treaties during those times. The Constitution places no limitation on when the President may convene either or both Houses. We therefore conclude that the President has the power to convene the Senate during the planned August adjournment.
WILLIAM P. BARR
Assistant Attorney General Office ofLegal Counsel
https://www.justice.gov/sites/default/files/olc/opinions/1989/07/31/op-olc-v013-p0245.pdf