The supercharger is a compressor. Air exiting it is under higher pressure than air entering it. Ford used such a setup successfully on the RS100 rally car. The supercharger gave the engine artificial size at low RPM, and the turbo was providing the boost at hitgher RPM. After a certain boost level, the supercharger WAS bypassed by the turbocharger, you are so correct about that.
With a large enough intercooler, the air will be close to ambient temperature when it enters the IHI blower, after which it will be cooled by the twin aftercoolers in the blower manifold.
When done with sophistication, the effect is that of just having more (in the case of this engine, monstrous) cubic inches. Even a properly set up ("setup" is a noun, "set up" is a compound verb) turbocharger system alone has this effect.
Would it not be fascinating to see a system where the boost kicks off an A/C pulley-style control that just cuts out the blower?
Actually, the effective compressor that is the screw blower on the Hellcat would better be replaced by an old-fashioned top-down Roots blower if this were the angle of attack one was going to use.
I'm just mentally tinkering with this. These cars don't need more power, but life isn't about NEEDS, is it? It's about WANTS.