Does time elapse when the player is in a menu in single-player mode?
Solution 1:
It doesn't count.
When you go to the achievement list (the rightmost icon in the icon list in the upper right) you can see how much time is remaining. You can also pin the achievement (magnet-icon) to always have it in sight while you play.
You will notice that the countdown is paused while you are in the Esc menu.