The least important? I have no idea what you mean. What sort of conditions, what level of player are you speaking of and what kind of scoring is one trying to accomplish?
I think with some of the new tees, Davis Love III would have a driver in his bag if he was to play Pine Valley today.
Whatever it is you are trying to get at, Shinnecock is indeed a course where hitting driver long and straight is important on a number of holes, on ones with open approaches but especially on ones where you need an aerial approach. I think hitting driver from the championship tees is key on nearly half the holes: 3,5,6,9,12,14,16 and 18.