I've been on the phone with AppleCare and they've confirmed that iOS 10.0.1 has a bug that prevents signing in to a Managed Apple ID through Setup Assistant. Trying to do so results in the error, "Could Not Sign-In - Problem connecting to the server." I don't have a clean 9.3.5 device with which to test, but we had new-in-box iPads with 9.3.2 installed and they do not exhibit this problem.
For now, the workaround is to skip the Apple ID portion of Setup Assistant and sign in to iCloud afterward via Settings. I'm also configuring our MDM's Pre-Stage Enrollments to skip Apple ID until the bug is fixed since we'll be using Managed Apple IDs for the vast majority of our school district's users.
