I view this action by the coach (police officer) as poor judgement, UNLESS he previously coordinated (and recieved approval) with game management. In that case, "Let the game begin!"
I disagree with your analogy. Pens and pencils are readily available at the scorer's table. Guns are prohibited in school zones without pre-approved authorization. (Was that intended as a sarcastic "tongue-in-cheek" analogy?
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Additionally, the original post indicated that this officer was probably not in his jurisdiction. Again, I do not see justification for him to "carry a piece" while on the bench, unless there are extenuating circumstances. I would argue that we are obligated to involve game management as part of an information flow. I know if I were game management I would want to be aware of this.