"They cringe at the thought of paying $130 a month for cable so Boorstin won’t miss Nationals baseball games. [...] With Aereo, baseball streaming site MLB.com, and maybe another app, they would gladly use the Internet for all their video news and entertainment."
Nope, if the Nationals aren't over the air in DC (likely not most of the time), and you live in DC, it will be blacked out. Aereo does not affect this in any way.