Will garage door insulation improve cooling efficiency?
Yes, insulation would help reduce heat transfer through the door enough to make it a worthwhile investment. Steel is a good heat conductor, so heat from the outside air is readily transmitted to the indoor air. 

You wouldn't have to purchase a branded kit, however. Simply fitting 1" or 1-1/2" extruded foam (or even Styrofoam) will do. The one you linked seems priced competitively, though. 

Make sure that you have good vinyl seals on the door as well. Airflow is much worse an energy waste than conduction.