Seems reeeeeeally unlikely. Iowa votes on Monday, February 3, amd Trump delivers the SOTU a day later. McConnell said yesterday that the trial’s likely to begin next Tuesday with a Senate vote on the rules that’ll govern the proceedings.
That leaves them with 11 business days (they’re off on Sundays), start to finish, if they want to wrap this up before caucus day. Even if they proceed at a breakneck pace, the fact that at least two new witnesses are likely to be called and deposed makes the chances of finishing so soon next to zero.
Bernie and Warren are going to be stuck in Washington the day Iowa votes. Trump will address the nation the following day as an impeached president who hasn’t yet been cleared, with Pelosi sitting right behind him.