I don't know enough about Benford's law to draw conclusions, but is N=O(1000) a large enough sample size to expect it to apply? My intuition suggests that if county size does not span enough orders of magnitude then Benford's wouldn't apply because the distribution might lie in one of the "spikes" of the Benford curves, rather than reflecting the average. For example, if many counties had a population size starting with a "4", you'd expect more vote counts to start with "2" (presuming each candidate received close to 1/2 of the votes).

Hopefully someone with a stronger math background can expand in a more fluent way :)