The purpose of cavity insulation is not to stop draughts, which generally occur between ill-fitting window and doorframes. However since it will fill the cavity and given that some air movement does occur in there, particularly when the wind outside is greater, it will have some impact.
The main purpose of the insulation is to act as a thermal barrier to transmission of conducted and convected heat from your warmer inside to the outside walls, where it is lost.
Don't know about the sound insulation question.