By the Senate’s rules, he needs unanimous consent to reconvene the Senate, which is not in session after the confirmation. They come back on the 19th. He prob will not get unanimous consent but who knows, he might get the 17 or so GOP senators to convict.
Edit: I downloaded Riddicks’ Senate Procedures, which you can get from Congress. On page 1088, there seems to be precedent for reconvening by the Majority Leader and Minority Leader
It looks like McConnell and Schumer need to agree and they can reconvene the session in the Senate. The House operates by different rules, and even though it’s in recess, it is still in session.
Edit: I researched the date and the Senate majority won’t switch to the Dems until at least Jan 20th. That’s when Georgia Is supposed to certify the runoff. Until then, McConnell has the ball and he recently reminded the senate about the unanimous vote needed to get back into session. There’s a whole lot of complexity on going into and out of recess and both the House and Senate agree legislatively on the dates. I think this is to prevent one party from reconvening ad hoc to pass some one-sided laws.
Edit: There’s a rule called Riddick’s Senate Procedure that makes the Senate different from the House. Currently, the 117th Congress is in session, but they took a recess until the 19th. Anyhow the rule does state that Senate actions during recess require unanimous consent, otherwise the Senate reconvenes on the preappointed time.
“The House and Senate differ, however, in their interpretation of the relation between a daily session and a recess thereof. The House considers its daily session to continue during a recess: the mace13 remains in its place at the rostrum and certain forms of routine business may occur, such as the introduction of bills and the filing of reports by committees.14 The Senate, by contrast, permits actions of this kind during a recess only pursuant to an “order, adopted by unanimous consent.”15 In this sense, although the House can be described as “in recess” between the time it recesses and the time it reconvenes, it cannot technically be described as “out of session” during that time. In the Senate, on the other hand, it might be considered proper to say that when the chamber is “in recess,” it is “out of session”