No, because the Gold Order isn't formally involved in the project. If something is said that the Gold Order would really like to know then it'd put them in a tricky spot.
Also, was there any kind of pre-meeting purely among College Wizards? Mathilde has told multiple of them that part of all this is a bluff that Humans know more than they actually do. And the best way to do that involves first carrying together all the knowledge that's actually there. Especially the knowledge that the Colleges in question are willing to share among each other, bit not quite yet with foreign polities.
No, Mathilde is trying to avoid creating any us-versus-them thinking. She wants it to be that this isn't the four factions of the Colleges, the Elves, Kislev, and Thorek, this is a ten different organizations meeting and cooperating as equals. Any advantage that might be garnered by getting everyone on the same page would be outweighed by any impression that might give of the Empire ganging up on everyone else.
Is it possible to choose "Ignorance" for now and then include one or more Magisters in the conspiracy on a case by case basis at a later date?
Yes.
What stops us from directly going to Dragomas and asking him in person on the down low?
Because that's the worst of both worlds. You skip proper procedure but you also go to the person that's most beholden to them.
And conversely, how does the Emperor knowing stop the four Patriarchs from needing to be informed enough to be able to protect their charges?
Dragomas has proper procedures he has to follow, the Emperor doesn't.