That's a better question: does dropping a cheap ethnic produce market into a neighbourhood that didn't have any cheap produce nearby before improve health outcomes?
Eating habits are cultural. People used to eating mostly cereal and bread throughout the day aren't suddenly going to start vegetables because vegetables drop in price and become more readily available and appealing for consumption. Humans are creatures of habit and social momentum.
What if in their neighborhood there are new restaurants with cheap, plant-based foods too? And if packaged food with refined sugars (cereals) and unhealthy oils got more expensive at the same time?
Humans can change their diets. It would help to be subsidizing healthy foods instead of refined sugars.