The third prong provides a ground path from the chassis of your equipment to earth. The purpose of the third wire is safety - so that if the chassis inadvertantly becomes hot a breaker trips, or at minimum the ground wire provides an easier path for the ac current than from your right hand through your torso and out your left hand resting on a grounded item (i.e. resulting in death, which will subjectively degrade the sound quality of your system). Obviously if you plug the female end of a detachable three prong power cord into a male receptacle on your equipment you won't be connecting the third wire to anything, so it is no different with regard to the third prong than if you simply laid the power cord on the ground next to your equipment. In short, no it will not degrade the sound or damage your audio equipment.
Power Cord Question
My system is more on the budget end but some of the components have detachable power cords with two prong connectors/terminals on the rear. I notice that most upgraded power cords have connectors that plug into equipment having three prongs. Can these 3-prong power cords be used to plug into the rear of components having only 2-prong connectors in the rear without hurting anything or degrading the sound? Thanks for your input.