They can if the supply greatly increases. That's among the reasons why a project longer the Triboro brings so much opportunity. Decentralizing New York real estate would drastically improve affordability.
I'm not saying this proposal is bad. I quite like it. But let's not get the causation backwards. Urban poor aren't poor because of bad access to transit. Urban poor have bad access to transit because they are poor. Building transit ultimately changes the real estate value along the line, temporarily makes everyone's rent cheaper, and permanently increases the population of the city.