The way gentrification currently happens in most areas is NOT good for a city's poor population because they can't afford to buy housing at the new higher prices.
IF whoever is in charge of urban development makes bold, progressive plans to accommodate and include those lower-income people, the new income from the higher home prices/rent may be able to finance housing designed specifically for lower-income families that are still integrated within the larger development.
Done correctly, it COULD be possible to improve the are for both the wealthier, and those on lower incomes,
with facilities that are available to everyone. This, of course, requires a certain attitude regarding what urban development is meant to achieve. It won't work if everyone simply wants more and more comfort for themselves without any concern for those who earn less.
In an area with a more egalitarian mentality, it might very well work. An example is the new Beltline development in Atlanta, where new housing along the route will be required to include a certain percentage of housing units dedicated to lower-income families.