I lived there for many years and can tell you that the Kennedys do not. Hammersmith Farm was previously lived in by the Bouvier/Auchincloss family (Jackie's family), then maybe a museum and I think now private residence.
Maybe there are some Kennedy's there, there are several buildings (I don't believe that though, and its not important), but its a driveway, not a street. Go there, you'll see.