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The problem with that setup is that most (if not all) TVs will not pass surround sound due to copyright infringements. The way around it is to use an optical cable from the mini to the amp.
 
I have a mini that serves double-duty. It's connected via HDMI to my HDTV and also via MDP > DVI to a monitor. An external drive connected via FW800 contains my collection of movies and TV shows, which are delivered via Plex to the TV. Work can be done on the mini using the monitor while a movie plays on the HDTV. I can run the mini from my MBP remotely from anywhere in the house using screen sharing. The mini is connected to the network wirelessly, but the internet connection doesn't skip a beat. The only issue I have is that when I take the Apple Wireless Keyboard very far from the mini, to control movie playback, it sometimes drops the Bluetooth connection.

I do exactly the same with a 11 mid model. It works great. Also my biggest problem is the wireless keyboard. Anything further than 3 meters will fail.

Very annoying.
 
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