And volunteered to have herself crucified in part to impress him, I suspect...
With regard to Danlan, imo the idea of her being a spy for Taravangian seems far too obvious. Yes, there certainly appears to be more to her than meets the eye. But the information that's been provided almost makes it too obvious that she's an agent for Taravangian. Compare the possible clues dropped for that connection with some of the other subtle hints that Sanderson dropped within the book. For instance, the hint that Shallan has her father's Shardblade literally comes down to a couple of lines where she starts to activate it while frightened by the Truth Spren, and then decides against it, all without actually saying within the text what it is she's thinking about. Or there's the hint that the king has the same abilities as Shallan. There's a seemingly throwaway comment early on by the king regarding some odd people he's seen that seems to merely be a part of his paranoia, and then there's no further mention of them whatsoever. And that comment is long before Shallan (who the reader ends up mentally linking with the Truth Spren) sees the Truth Spren for the first time. It requires either a long memory on the part of the reader, or a second reading of the book, to make the connection between Shallan's Truth Spren and the mysterious figures that the king mentions to his uncle.
With Danlan, on the other hand, we're constantly told over and over that she's "special". There's nothing particularly unsubtle about her presentation, and as a result making her Taravangian's agent in the camp would be a waste. A spy shouldn't be anywhere near that easy to pick out.