The Queen's address to which Boris Johnson refers is a traditional speech by Elizabeth II, in which she presents the national political priorities conveyed by the Prime Minister. It was to prepare these famous priorities that Boris Johnson asked to adjourn the parliamentary session. A perfectly normal step in a new appointment of Prime Minister.
About this famous speech by the Queen, here is what Mr. Johnson told the British media on the plane to New York:
I am waiting to see what the judges decide (…) because as I said before, I think the reasons (…) for wanting a speech from the queen were very good.
It implies that, even if the Supreme Court would be wrong, he does not intend to resign. And even if this would be a new disavowal for him, a few weeks after the parliamentarians passed a law requiring him to seek a postponement of Brexit in case of absence of agreement with Brussels.