No, he's going to wait until Thursday. I actually don't think he's going to fire Rosenstein or allow him to resign. He's just trying to drum up a competing story to distract from Kavanaugh if the testimony goes badly for him.
My guess is that tomorrow's press conference is going to be a similar move. He'll drop some line to try to create a competing news story. This is likely a move intended to try to overshadow whatever Avenatti has planned.