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Remember, the larger the tire, the less grip as measured in lb. per sq. in. due to the contact patch and putting a narrower tire (same circ.) increases grip for the same reasons. Just some food for thought.

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Given a perfect world. Of coarse it has to. Everything else is constant.. Say same HP, same weight same compound, it has to "Try" to plant the smaller foot print, of coarse it has to "Hold" more than a larger foot print tire. That's the point of larger tires, less force for a given area, means less likely to spin.
Its more like Cohesion than adhesion as via Velcro.
Fact is you use a good 13x31 or 14x32 tire on the car it will be more consistent in any track condition, you might give up a little e/t due to rotational weight etc, which if your spinning on a marginal track what e/t is there anyways to loose except for the round of coarse.