Not, the Airport Extreme, only the Airport Express. Use the Express if you don't have a TV connected to this system. If you do have a TV, use the AppleTV.
With the AppleTV, you can connect via HDMI, or with either you can connect with a pure digital toslink connection if your stereo supports such a connection.
And these require no physical connection from the iPad. They connect directly to the sound system, and your home network, and you then use Airplay on the iPad to send the music to the device.