Well, the Umbral Era quests are those telling the story of Dalamud - and those are confirmed to be removed in 2.0 (since the story in version 2.0 takes place after the events of Dalamud). The whole draw to the game currently is to experience these events as they unfold, as they will be over with and gone in 2.0.
As for the main story arc, that is unclear however they say there is an all new story line planned for the new version of the game so the new story could either be an addition to the current story or replace it entirely (in terms of being able to experience it).
