Most people (including you, and most of the cops visiting the coroner) wouldn't eat something while examining a dead body, be it for hygienic reasons or because they're disgusted of dead bodies. So first of all seeing him eat something while examining a corpse infuses some kind of awkward feeling, making the coroner stick out from us normal persons as kind of living in his own world of dead people. In contrast to you and me (and the cops) he is used to hanging around with dead bodies and finds them so normal to not shy away from eating in their presence, which in turn makes him look non-normal to the average audience and the cops.
What this in turn means for the characterization of the coroner and this situation probably depends on the overall tone of the movie or situation. This awkward or unique image of the coroner can be either somehow scary, or rather comedic, or just depicting him as belonging to a professional elite, being a pro at what he does and different from the average cop (a "squint", so to say).