So, for me the solution was to start from scratch with a new Unity project on a "known stable" version of Unity. Re-using old projects appears to be a bad idea (maybe old/incorrect settings buried somewhere).
Hopefully this post will help someone else who runs into the same problem as I was - unfortunately I don't know if this is relevant to the original post as I'm not sure if @JensPeterson is using Unity for their application.
Original post below:
Hey there, I'm getting the same issue on two different iPads - one on iOS11 beta, one on iOS10.3.3, same as @JensPeterson.
The other existing Structure Sensor apps work fine - both the Calibrator and the Room Scanner show the sensor is connected, but the example SDK apps just always show the "Please connect Structure Sensor" message after initializing the camera.
I'm using the 0.6.2 SDK on example SDK apps built in Unity 5.5.0f3, which was suggested in a different thread as the last recommended Unity version - I rolled back to this from Unity 5.6.2f1 after seeing the same issue when building the example apps. This is all being built on a Mac Mini running XCode 9 beta 3.
Since this is the first time I've tried building the example apps, I made sure to follow the included PDF guides and I've double-checked all the Unity settings, but still can't get the example apps to believe that the Structure Sensor is plugged in.
Edit: Building the sample Viewer app in XCode 9 beta 3 and deploying to both iPads (iOS 11 Beta and 10.3.3) works fine, so it seems to be a problem specific to Unity, or the Unity examples, not the hardware, iOS or XCode.
I'm going to try a clean install of 5.5.0f3 and do everything from scratch with an empty project (my current project was based on an existing one that I imported the Structure UnityPackage into).
Edit 2: I think I've finally found out that it appears to be my Unity project setup (maybe corrupt/damaged due to being made on a newer version and opened/build in an older version?). I did a complete fresh reinstall of Unity, and set up the example UBT scene in a fresh blank project - this built and ran fine even on iOS 11 Beta, and detected the Structure Sensor! Yay!
Then I tried using the same setup to build my original Unity project (same Structure UBT example package imported, same Example scene) - but it never detects the Structure Sensor even after it's been plugged in.