There have been studies done regarding sensory deficits during stressful situations (of which auditory exclusion is one such phenomena).
One of the interesting results that have surfaced over the years is that specific & proper training can, in effect, help "inoculate" some people against some of these sensory deficits.
Cognitive functions may be depressed (the lizard brain surfaces, as was mentioned, and people often go into "freeze, flight or fight mode"), but the ability to access and engage training that's deeply ingrained can be cultivated.
Operating on just any sort of unplanned "instinct" can get you killed, especially if the "instinctive action" which the person's lack of experience spits out is counter-productive for survival under specific circumstances.
Being able to effectively access & employ properly ingrained training during moments of high stress is still going to require the ability to make good decisions, though.
Being able to function while experiencing the psychological and physiological effects of unexpected stressful situations (including the effects of the hormonal fear response) can be unpredictable for people, especially if they're untrained & unprepared to face such situations ... but good training (both initial & recurrent), has been found to be helpful.
Memory, and being able to access it, is another subject.
Retired LE - firearms instructor & armorer