I've only ever seen one unintrusive animation in UI, which was the window minimization animation of the Metacity window manager. It minimized the window immediately, but then followed up with an animated outline showing where the window had gone. It was thin enough that you could easily ignore it, but still provided all the benefit that designers claim from their slow and disruptive animations.
Edit: Exact test of rule 2:
Productivity soars when a computer and its users interact at a pace (<400ms) that ensures that neither has to wait on the other.
Nowhere does it say that waiting is only bad if you don't see something happening. I am waiting on the computer to finish it's little jig. That is bad, and a violation of rule #2.
Further, from the original study itself:
"When a human being’s command was executed and returned an answer In under 400 milliseconds, it was deemed to exceed the Doherty threshold, and use of such applications were deemed to be “addicting” to users."
My answer has not been returned within 400ms, this the Doherty threshold has not been met.