I have no idea why this works, but if I throw/slide my Google Nexus 9 tablet onto my old iPad 2, the iPad wakes up and logs in automatically. You can see it happen in this 30-second video:
I’m not touching any iPad buttons when this happens. My guess is that the iPad 2 thinks that I just removed a magnetic cover, but really, I have no idea why it does this.
It’s important to note that I don’t require a passcode on my iPad. I set a passcode on it and tried the same thing, and it just brings up the passcode login dialog (which is a good thing).