OK, let me refine my point:
If you hooked up the supercharger and set it to produce zero psi, you aren't going to damage your engine.
If you hooked up the supercharger and set it to produce .5 psi, you aren't going to damage your engine.
If you hooked up the supercharger and set it to produce 10 psi, you are probably going to blow up a whole lotta stuff!!
Somewhere in there exists a happy medium where power, fuel economy, volumetric efficiency (VE), etc are all increased because the s.c. eliminates the effects of things like barometric pressures, gravity (which also effects things like air and gas charges and the way they move) and especially the viscosity of the atmosphere which all make a naturally aspirated car run somewhere well below 100% VE. I think most cars are about 75%-85% volumetrically efficient.
I'll try again to put it in simple terms for an example. If your car has 1000cc engine, naturally aspirated (NA) it will use about 750-850cc of combustion space where as charged it will use the full 1000cc or even more (the "even more" is where people get into trouble). On a NA car as the engine moves through the power cycle it creates a vacuum in the combustion chamber. All that induces the charge into the cylinder is this barometric low spot, however, it has to "pull" the air/fuel mixture in to fill the void. Under normal conditions it can't do this fast enough which is why you only get 75%-85% sucked in there before the valve closes and the piston starts the compression stroke. Adding a turbo/supercharger gives the ability to force the air in faster and fill the full 100% of the cylinder during the intake. With smaller pullies and therefore higher psi you can even increase VE up to 110%-120%.
NOW, all that said, it is up to YOU to decide how you want to use your car, how sturdy the internals are to begin with and how you're going to drive it. Those factors are all independent of the benefits of charging.
JACK