No, they have debuggers and modern dev tools. They just prefer to read code from paper when they have to really focus on it for a long time.
>then they annotate it with a pen while thinking about whatever problems they are solving.
Paper and pen offer a lot of options you don't have in vim (or emacs/notepad.exe/etc ;)). Circling, doodling, arrows, underlining, furiously scribbling...