Would Japanese reinforcements let Hood enter refit?
Short answerPossibly. More fast capital ships could cover Hood's absence, although Britain could also postpone refits until the German surface threat had been defeated.
NotesIf a German sortie waited until May 1941, the Home Fleet could have King George V and Prince of Wales alongside Japanese Kongō-class ships. Force H could add Renown, another Kongō, and more carriers if Italy had left the war. That strength would make Hood's historical role alongside Prince of Wales much less likely and could allow her engines to receive attention. Nagato and Mutsu could also provide cover while Nelson or Rodney entered refit. An alternative would be to retain the available ships until Germany's surface fleet had been defeated, then undertake the work with less urgency.