Would a few carrier fighters have been enough to save Force Z?
Short answerThey might have, because disrupting a coordinated air attack could make its individual elements much easier for the ships to evade or repel.
NotesEven a modest fighter group from a carrier such as Eagle or Hermes might have broken up the attacking formations. Warships could better concentrate anti-aircraft fire and maneuver against aircraft arriving one at a time than against several coordinated attack axes. Interwar naval air doctrine recognized that massed aircraft were needed to overwhelm a defended ship. Fighter cover therefore offered Force Z a chance by disrupting concentration, without requiring every bomber or torpedo aircraft to be shot down.