In case anyone was wondering, the Lightnng to 30-pin Adapter works great with the original iPad Keyboard Dock and an iPhone 5. In fact it is better than the 4S was, as that tended to pop out. The Lightning adapter stays in place, and there is plenty of support in the back plastic to keep the iPhone in place, with any tiny stress happening at the Dock connector end: the Lightning connector itself seems very solid indeed. All the keys work, and charging is fine.
(In answer to the implicit question: my employer blocks email at work on its systems, and it's convenient to have the keyboard hold the phone in place, and also charge it, which is the problem with the Bluetooth keyboard.)