Extra time when time is of the essence (U.S.)
Do current accommodation policies recognize a "special kind of tests"
  where "time is of the essence" and requests for extra time from
  students with disabilities can legally be turned down?


No. 

For example, where I am, instructors receive a form simply saying, "Student X has a right to double time on exams". There is no sub-categorization made to that right, and no channel for instructors to pick or choose whether to honor it.