My skepticism is mostly around not the economics but the sheer accumulation of desperation in these small communities creating high corruption and theft rates ruining the efficacy of the concept.
When you take into account the amount of energy required to grow food, refrigerate it, ship it halfway around the world, and distribute it to stores, surely the amount of energy required to grow food locally is inconsequential.
You're still going to have to refrigerate and ship the stuff locally; Train and ship shipping are relatively cheap compared to the last mile shipping.