For the Display, Yes if your graphic card/mobo have HDMI output.
For the Sound, it depend on which card u r using. If u use old nVidia cards, they don't have a built-in sound processor and u have to connect ur sound card to it in order to carry the sound signal through HDMI. For most of the Radeon cards, they come with the built-in sound processor and shouldn't be any issue. Just have to select correct sound output from the CCC.