Javik and Leviathan aren't essential, without them we don't have an incomplete story. They add almost nothing (they added some useless background, which isn't the story).The DLCs actually break the structure of the original game which was very well balanced, so they don't complete the story, they destroy its structure.
I don't really buy into this uselessness bit, since lots of lore, character backgrounds and such are generally there to simply expand the universe a bit more to pique the player's interest. That they don't play pivotal roles in the main plot doesn't make them useless.
As for structure, it's not like that's ever mattered. As an interactive story, the structure is what we make of it. ME3 may be more linear than the other two games in the way missions are set up, but there's no set structure that Javik's mission or Leviathan totally disrupt. I mean really, how is Javik's mission any worse than, say, N7: Cerberus Abductions?
The only one that I can honestly say creates a real disconnect is the Citadel DLC, as it's so tonally different from the rest of the game.
This kind of reminds me of one poster on here who roleplayed ME1 where it made no sense to do anything other than the main plot missions, and he never returned to the Citadel at all until the game gave him no choice. He argued that flying around doing this and that totally destroyed the story, and it was hard to argue against it considering it was called a "Race Against Time".