Nah mate, I haven't used the case once, they're still in the box under my bed. Just had the APM dangling off my stand, they were connected to everything still. Mac was running in the background.
The first time around I was just starring at the firmware number on bluetooth settings, hoping for it to change nothing happened.
I believe the OS needs to believe that your devices aren't going to be used for a while whilst it undertakes the update. I'm guessing the last thing Apple wants is user wanting to use their APM whilst its going through an update and the user believing theres something wrong with them, pressing buttons here and there, disconnecting bluetooth etc. which may cause some issues.
I suggest just leave them for a couple hours with your phone untouched, see what happens.