All Seeing Eye
Admiral
If your suggestion is correct then that would mean the following:
1. It takes a good amount of time, hours for instance, to reach max warp because Sulu says "Engines at maximum warp" just before Chekov announces the mission.
2. Chekov announces the mission hours after departure and minutes before arriving at Vulcan
Just because Kirk is sedated doesn't mean he has to be out for hours. Maybe subconsciously the mention of 'lightning storm in space' woke him up straight away.
Good points, also if Earth received a distress call from Vulcan that means Nero has already fired his drill. How long would it take for a weapon of that magnitude to drill to the core? less than hours surely.