I doubt sprinklers would have had much effect given the vector and rate of fire spread. They only have them in plant rooms and industrial kitchens. Sprinklers might have suppressed a bit of smoke in the corridors, but the fire spread up the outside, not the inside due to superheated air rising between cladding and concrete.
The problem appears to have been the alleged failure of the alarm system, the alleged emergency lighting failure and the single fire evacuation route, completely inadequate for a tall block. The whole place was 'dead end condition', hampering escape by the people and access by the firefighters.
