While I don't live in a food desert where these kind of stores are the only option, I have, in fact, regularly found plain yogurt in gas-station convenience stores, the even smaller refrigerated-food sections in urban drug stores, etc.

Now, fresh produce, except—if you are very lucky—extremely expensive (for the quantity), relatively small packs of cut carrots and other things people might reasonably purchase as snacks, anything usable as a cooking fat excepted salted butter, and lots of other things, sure, you are going to be SOL, but plain yogurt (both the usually watery American kind and strained "Greek” yogurt) seems pretty common.