Quite true. Takes quite a long time for any benefits to show though and by then the myriad corpses produced by the ensuing starvation are doing much more for the biosphere then the ash.
I don't think starvation is going to be as major a threat as you think.
This is not 10,000 years ago, we have winter clothing and heating. Also, we have other ways of getting food, besides crops and cattle from our own country. We may have to do some major fishing in the deep oceans until the sun shines again, in a year or two. But most of us will not die.
On other note, when this does happen, the United States as a whole may learn a hard lesson in who are friends and allies in the rest of the world really are.