What constitutes the "completeness" of an app for eligibility in testflight?

Solution 1:

This information is detailed by Apple on their Testflight page.

When you add the first build of your app to a group, the build gets sent to beta app review to make sure it follows the App Store Review Guidelines. This is the only beta version of your app that requires a full review, and testing can begin once it’s approved.

Drilling down into the App Store Review Guidelines under Beta Testing, there is this statement:

Any app submitted for beta distribution via TestFlight should be intended for public distribution and should comply with the App Review Guidelines.

Bottom Line: Your Beta app is going to get reviewed once, and the expectation is that it's "ready" for distribution. An app that doesn't function is, by definition, not ready for distribution.

You will have to use an alternate distribution method if you want to get out incomplete - totally non-functional builds.

Get devices and load them from Xcode and ship them out or have people ship you their devices is the next best method if you don’t want to use a wireframe / mock up tool to get past the initial design phase and you have a minimum viable product to share with Apple for Apple hosting and distribution to your test group.