A: Yes, that’s exactly what she can do, in fact, this is exactly how the Secret Cultist was meant to be deployed. Otherwise it doesn’t do anything at all, if you think about it (except hurt the holder in much the same way as the new Secret does if revealed). More technically explained, as a Surprise card, it’s meant to be played out of turn, including, in this case, specifically just after the game has “ended” due to an UnGoal.
The Secret Cultist, is, naturally, working for the downfall of everyone, staying hidden until the Old Ones rise to take control, at which point they come out of hiding and claim at least enough credit so as not to get destroyed.
Sorry to break it to you… Thanks for playing our games. Maybe she can put in a good word for you after the apocalypse or something.