That's going to be up to them - are they going to work WITH the neighbors in Central, or are they going to charge merrily along without addressing the concerns?
"Gentrification" in this case is a really gray area. On one hand, if they just go do whatever they want to do without supporting the neighborhood, they're asshats and a detriment to the community. On the other, if they are good neighbors, despite great prices on some items and very expensive prices on others and everything in between, they still can be a really good thing for many families there who just don't have access to fresh food without a major effort.
I don't believe things have changed much in terms of groceries since I left. We had a horrible market on the other side of 35 on Lake, which sold rotten/spoiled food in filthy conditions. They weren't cheap, either. Las Americas on Lake wasn't full service, and sadly unless people spoke Spanish, they mostly didn't go there. Plus, not cheap. You could subsist on convenience items from Cup or a couple other relatively nearby stores, but that was very expensive and mostly junk food. You could travel several miles down Lake in either direction to a Rainbow, or to Cub towards the river. For a lot of people, especially feeding a family, that was a long hike by bus for not a lot of groceries that could be easily brought back. Way back, I drove taxi for a while and remember how desperate some people were to maximize their bang of travel cost versus what they could afford to buy and what they could manage to bring back with one or two people. These days, Cub and Rainbow have somewhat cleaned up from when I lived there, but the Lake Street locations still have a ton of processed food vs. fresh, and the quality of veggies and fruits still were not so good. Earlier on, I had to avoid buying cold cuts, sliced cheese, and most dairy, and had to be very careful in buying meat - more than once I got home and the product was already bad. I'll never forget the turkey that looked nice on one side, and was green on the other.
Grocery stores are such a big deal for city dwellers. People in my neighborhood couldn't afford Lund's or Kowalski's or Whole Foods. You'd think that Cub or Rainbow, which had really nice food in some of the more suburban areas, wouldn't send all their awful stuff to these stores that blatantly, but they did. It's amazing how grocery stores are the biggest sign of racism and classism in these areas. You get nice stores in the vicinity, but they're only for the wealthy folk who can pay double what they'd pay at the other store 2 blocks away. So, I want to hope for Seward being a good guy instead of a bad guy. I guess only time will tell.