The pump pushes water into the tank compressing the air bladder until it reaches the upper pressure setting on the control. This also has the advantage of storing some volume of water in the house so that the pump doesn't have to turn on to provide pressure. Assuming that the pump control is working (it turns off at the proper time), you won't blow anything up! I'm not sure how a pressure tank is specified - there is probably some way to calculate good turnon/turnoff set points and size of a tank to provide a reasonable volume to minimize short-cycling the pump.
Having no air in the tank causes many problems as can having the wrong pressure in the tank.