Not according to Wright v United States. It basically takes the same assumption as you are making but reverses it. Congress IS in session unless both houses adjourn.
They wrote in reference to a similar scenerio:
“The Congress’ did not adjourn. The Senate alone was in recess. The Constitution creates and defines ‘the Congress.’ It consists ‘of a Senate and House of Representatives.’ Article 1, § 1. The Senate is not ‘the Congress.”
So if only one half of Congress adjourns but the other has not then Congress as a whole has not adjourned. At least that’s my understanding of it. If I’m wrong, please do explain. I’m not a lawyer, that’s why I’m throwing this out there.
My thinking is that “Congress” cannot act unless both Houses are in session.
The Constitution limits the amount of time which one house can adjourn without the permission of the other to three days. So this issue is of interest only for three days.