He's still not questioning the fact that she's never said a word. Not even asking if she's unable to or anything. That's my main issue with this part of the story... well, one of the two big ones. There's also the issue about how she's not willing to come clean, I mean, come on, she's fully aware that he's madly in love with her, she's got the same feelings, they've banged once already, and he's got enough trust in her other self - both as a person (based on how much he's said to her privately) and in terms of competence as a whatever-her-role-is (based on the missions he's sent her on) - that there's little to no chance he'd push her away or fire her/lock her up/whatever. Worst case that's at all likely is him being a bit awkward around her when she's acting as a guy for a while, or maybe asking that she retire to just be his wife, the latter, I mean, is kinda not great, but she wants to be with him. Best case is she gets a promotion and a half, to where she's more of a live-in guard (publicly, as a guy) and a wife (maybe also publicly, under the name Yeon).