Food DISTRIBUTION is not the issue. Nor is "dependence on agriculture" the issue. Just as the people of our culture believe that we are humanity itself, we have the idea that the agriculture we practice is agriculture itself. Let's start with that. Agriculture is simply a means of promoting the regrowth of the foods people favor. In that sense, virtually all Leaver peoples practice or practiced agriculture. But merely promoting the regrowth of the foods you favor doesn't automatically make you totally dependent on agriculture. One people may grow very little; another may grow a bit more; another a bit more still; another quite a lot. There is no single degree of production that makes you an agriculturalist. (Even we don't grow 100% of our food.) Leaver peoples around the world have lived for thousands of years as agriculturalists (to answer your question about whether it's "possible for a society dependent upon agriculture to live sustainably").
We practice a unique form of agriculture that I've called Totalitarian Agriculture, which is based on the idea that, since the world itself belongs to us, all the food in it belongs to us as well. In other words, we can (1) take any food formerly available to other species and lock it up for our exclusive use, (2) destroy any species that competes with us for our food, and (3) clear any piece of land of food formerly available to other species and use that land to grow food for our exclusive use.
Totalitarian Agriculture began to be practiced among us at a time when the world wasn't thought of as having any limits. It was assumed (even if it was never explicitly so stated) that the world was of infinite extent, and if this were the case, there would be no problem. In fact, however, the world is a place of distinctly finite limits. There is only so much food-bearing land (land that will sustain life) and only so much food-bearing water. We can't increase either of these commodities (though we can reduce them and ARE reducing them), and we can't increase the amount of sunlight that falls on our planet, from which ultimately all life (and therefore all food) derives.
Here's another way of saying this: at any one time, there's only so much biomass on earth (biomass being the mass of living material). The amount of biomass varies, but only over very long periods. When we cleared the Great Plains of all the plants and wildlife that was living there and converted this land to the growth of human food, we didn't increase the biomass of this region, we merely converted the biomass that was already there into human food (and ultimately into human MASS).
Three million years ago, the percentage of biomass that was human mass was negligible (perhaps equivalent to the biomass of gorillas today). Ten thousand years ago the percentage of biomass that was human mass was still very small. But with the advent of Totalitarian Agriculture, that changed very rapidly. Humans (of our culture) now account for a very sizable percentage of the earth's biomass (and that percentage increases daily). It's estimated that, with our population at six billion, as many as 200 species become extinct every day as a result of our impact on the world. When these species become extinct, their biomass doesn't disappear; it's simply converted into human food and ultimately into human mass. When we cut down a million-acre rain forest to put the land to the plow or to turn it into pasturage for cows, its biomass is turned into human food and ultimately into US. As our population increases, the number of disappearing species will increase (and probably geometrically).
Even though there are hundreds of millions of species, it can't be imagined that eliminating 200 every single day is a sustainable way to live. The community of life as a whole is what makes this planet livable, and it's absurd to imagine that we can reduce that community to ourselves and a few hundred food species we like to eat. We're like people living at the top of a tall building who every day go downstairs and knock 200 bricks out of the walls here and there. For a time (since there are hundreds of thousands of bricks in those walls), no change appears. But if this goes on long enough, the structure itself must inevitably collapse--and not in a gradual way. We live in a period of mass extinctions, brought on by our own actions, estimated to be a thousand times greater than in normal times. The victims of this mass extinction are not just going to be species we imagine we can live without (hornets, rattlesnakes, gophers, sharks, rats, poison ivy), they're going to be species upon which ALL "higher" life forms depend--including us. It isn't as though we're able to pick and choose which species are to disappear. Ultimately, if we go on in this way, the human species will disappear along with the rest, leaving the cockroaches in command.
This by no means answers all questions on this topic. Those who want more information might have a look at FOOD PRODUCTION AND POPULATION GROWTH, a three-hour video I produced with conservation biologist Alan D. Thornhill, available at http://www.newtribalventures.com/market/.