So, the following information may be dependent on which IA ending you got. As such, I am placing some of the following behind spoiler tags.
Based on that conversation, the establishment of a new intelligence organization, presumably "Sith Intelligence," is heavily implied. Since both sides are now officially at war, the Sith has lost over 1/2 their Dark Council, the Emperor isn't making any press appearances, and the Empire pretty much got their @ss handed to them due to their own ineptitude, even if the Sith wasn't planning on having a successor organization to IA, they aren't going to have much choice now if they are serious about winning.
Sure, it's possible that they will try and muddle along, using the military and freelancers for their covert needs. Oh wait, yeah this is the incredibly paranoid, xenophobic Sith we're talking about, right?
As disorganized and self-destructive as the Sith are, I would find it very hard to believe that Intelligence of any kind would just go away. More likely there will be an organization where the Minister is a Sith, or reports directly to and take orders from Darth so-and-so Scary-Pants. Since we have yet to see how the Dark Council will replace the recently deceased, it's logical that someone we have yet to meet will take the reigns and try and rebuild. That will be a cut scene I look forward to.
Are there breaks in logic in the IA story? Sure. Is there a ton of stuff we as "The Agent formerly known as Cipher 9" don't know? You betcha. Do any of us really know what will happen in Chapter 4? Hell, I doubt Bioware even knows at this point; but they have promised that the story will continue. As a whole. I didn't find the story arcs that unbelievable. But that was kind of the point of the story. You never know what is real, or who is really on your side. More often than not, it's your ally stabbing you in the back rather than your target. That's the life of a spy. *shrug*
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