It would depend entirely to whom you were a secretary. Are you General Groves' secretary? Then you know. Because there's no way you can type out all of the memos he is dictating without seeing some quite frank references in there (Groves did not do his own typing). Groves' secretary, Jean O'Leary, had a desk right next to his in his office. She had, at the age of 30, been made a widowed mother when her husband died of leukemia, and applied for a government job. Groves had gone through several secretaries before finding her, and as Groves' biographer Stan Norris described it, "she was the only other person who knew almost as much about it as Groves himself." She acted at times as an executive officer, making decisions when Groves was out of office. Norris notes: "At times there were minor problems with some male officers who would not fully respect her or take orders from her. Groves had wanted her to join the WACS the Woman's Army Corps hoping that a uniform and rank might correct the problem, but it never happened." (Norris, Racing for the Bomb, 7-8.) She also took shorthand notes on basically every phone call that Groves had. She was in the loop. She was the only other person entrusted to an entire set of the "codes" that allowed one to make sense of the many codenames used during the project.

Are you the secretary of someone in an OSRD section unrelated to the bomb? Then you have no idea, of course.

Are you the secretary to someone who is somewhat more peripherally connected to the bomb? Then maybe you know some things, maybe you don't. I get the sense that O'Leary was exceptional, but surely the secretaries of people like Vannevar Bush would have been somewhat aware of the nature of the work, since they typed out memos that at times make it quite clear.

You won't have gotten some big briefing on it. You'd be picking up things just from memos written out. In one of the files I've seen, I believe it was James Conant's secretary who kept mis-spelling the word "fission" as "fishing" (they do sound quite similar) which the scientists found endlessly amusing.

You would not be part of conversations, you would not be encouraged to give an opinion, you would not have the full picture. You'd have slices and bits and pieces. I suspect you'd need to be quite high up to see things that looked like "big picture" and didn't look like, "increasing the production schedule of Tuballoy at X by 3.5%" and other technical and code-named jargon. You would not be having moral conversations about it; you wouldn't be discussing the plans for the use of the bomb at all. Interesting, the memos of meetings that had that level of discussion, like the Target Committee meetings, were taken down exclusive by male participants (soldiers, usually).

It is not clear to me how much scrutiny these secretaries got, beyond their initial security screenings. Of course, in retrospect it is easy to see that such a person would be a perfect vector for espionage, but I'm not sure they were quite as hip to that at the time — they put a lot of effort on the gut-feeling approach to "trust." But it would be interesting to see if there are FBI or G-2 files on secretaries; I've never looked.

The best account of a Manhattan Project secretary is that of Ms. O'Leary, in Robert Norris's Racing for the Bomb: General Leslie R. Groves, The Manhattan Project's Indispensable Man. The difficulty, of course, is that O'Leary (and Groves) were at the very tip of the top, and so their situations are likely highly unusual and anomalous.