interesting question.
According to this article, Senate can be/is in session:
WASHINGTON (AP) — Kansas Sen. Pat Roberts was in session briefly by himself in an otherwise empty Senate chamber during the federal government’s partial shutdown.
The Kansas City Star reports that Roberts and his wife came Thursday to the Capitol for the Senate’s afternoon session while colleagues in both parties remained away. The session lasted only three minutes.
Roberts and his wife have a home outside Washington. He hurt his re-election bid in 2014 by being registered to vote at a friend’s address in Dodge City, and he bought a home in Topeka in 2016.
The 82-year-old, four-term Republican hasn’t decided whether to seek re-election in 2020. Roberts told reporters as he was leaving the Capitol on Thursday that he will return to Kansas to meet with his family and campaign team.