Without doing all the calcs I can't say absolutely yes, you could run midgrade or regular, but the IC's job is to reduce temperature gain from pressurization. So the air going into the cylinder is starting at a lower temperature than if it comes straight off the supercharger. If you have the values to plug in, then you can calculate the temperature of the mixture when it is fully compressed. If the IC removes enough heat to keep this temperature under the autoignition temperature for midgrade or regular, then it's OK to run the cheaper fuels. You can do the same thing with water or methanol injection: remove heat through the heat of vaporization for water or methanol (or a mix of the two), and sneak under the premium requirement.
I like the IC idea because you'll never run out of IC, where you might run out of water or methanol, so you need some kind of warning to let the driver know the secret sauce needs a refill before the engine gets mad and holes a piston.
Any FI setup needs a way to comtrol the intake temperature because intake air always gains heat under pressurization. It's one of those immutable laws of physics.