So tptacek is correct that a farm inside a grocery store does not solve grocery affordability for the poor, because the problem is due to transportation/access, not the cost of the goods.
The bridge between these two views would maybe be if there was a solution of vertical farming that used little real estate and was able to set up a vertical farm in a poor area and had minimal real estate footprint/low rent costs.
Paper on Food Deserts in Chicago (or just google "food deserts chicago"): http://www.usccr.gov/pubs/IL-FoodDeserts-2011.pdf
I'm not sure if you shop mostly in Whole Foods or buy individually plastic-wrapped bell peppers at Trader Joes, but go to a Mexican grocery store some time and fill a cart full of green things. Vegetables are very cheap.