I rewatched "Magic to Make the Sanest Man Go Mad" last night, and had the same thought.
It probably wouldn't work, because that "secret" was so strongly tied to Burnham's emotional state on the night of that party, but...honestly, that makes me want to see the scene play out even more.
Same here. I felt that saying that and having it not work before Rayner has his big speech would have been more fulfilling, and it would have tied in with the awkward scene about pretending to still be in a relationship with Booker.