That's a different design; Audi uses a separate electric supercharger to fill in boost while waiting for its conventional turbochargers to spool up. Porsche is using a motor/generator built in to a turbocharger to spool it faster, and to recover energy at maximum boost.
I was thinking of that when I wrote the comment! I've heard of electric turbochargers, but I'm not sure how good they are under real-life conditions. Directly using heat energy from the exhaust (as opposed to introducing electric conversion losses) seems wiser to me. Part of me has always liked making use of what would otherwise be wasted to entropy.
In theory (though not a mechanic, just have an interest in this), the best middle-ground would be to retain the same design but add a motor to the turbocharger shaft which would mainly be reserved for spool ups -- is that what they're doing?
What you've described is exactly how the F1 MGU-H works (as I posted below). F1 is getting rid of it next year because it costs too much for an F1 team which should tell you a little bit about the complexity involved.
GM is doing nothing of the sort, it's just an ECU map. Guessing here, but if driver presses on the gas quickly (throttle accel > some set value), juice the engine map to create extra exhaust pressure to spool up the turbo impeller. It's all software.
