Transmission yes.
Fuel pump no, you can start it and run it on it but at full throttle it cant supply enough fuel and it will lean out.
As explained in other threads, the supercharger does not make boost all the time. Its controlled by a bypass flap which is actuated via manifold Vacuum. I feel your having great difficulty grasping the concept of how it works.
No throttle = high manifold vacuum -
The engine is trying to suck air in through a straw essentially so it builds manifold vacuum and this pulls the bypass actuator open so the supercharger just pushes air back around intake side of the rotors instead of down into the cylinders and can never make any boost pressure.
Half throttle = low to no manifold vacuum/starting make boost
The bypass valve will start to close because it does not have enough vacuum to stay open due to the amount of restriction created by the throttle body being reduced, this allows the supercharger to create some manifold pressure as its no longer pushing air back around onto the intake side of the rotors and also pushing in more air then the engine can use but it cannot draw enough air through the half opened intake to create maximum boost - basically.
Full Throttle = no mainfold vacuum, its under boost-
The bypass is fully closed allowing no air from the supercharger back around to its intake side, the supercharger will now draw in as much air as it can and create as much boost pressure as it can as its fully unrestricted. The faster the Supercharger spins relative to the engine dictates how much boost the supercharger can make. Obviously a larger charger moves more air hence it can create more boost on the same sized engine. (mods like higher ratio rockers, cams etc will reduce boost as the the boost pressure has more of an opening to escape down the exhaust pipe during valve overlap.)