Do secret rooms work? And if so has anyone had experience with them?

No they do not. The treasure chest, secret room, and nothing cards are to be removed from the search deck when playing RtL.

Is this due to lacking the feature in the app? I really love idea of the secret rooms and treasure chest and would love to use them.

The app is not designed to handle these cards. It is not built to track the shop draw, the additional tile, or remove a challenge token per round.