That it would.
Frankly speaking, in the horror games, reaction of the characters goes only as far as the players perceive it should go, and in my experience, majority of the "horror" stories that try to force the "mood" on the players are more frustrating than actually disturbing.
So might as well make that(ability to give a level appraisal of events) a defining feature of the character, instead of making a "normal guy" and then dealing with the accusations of not roleplaying properly.