Yeah it should work. You'll just have to change which monitor you want to use manually between one of the DVI outputs and the HDMI output. Although I have to point out, since your not going to game, why the 7970? If you went with a cheaper card you could almost build a second dedicated HTPC. Just a thought.
I have the same card, there are 4 different connectors (2DVI, 1 HDMI and 1 Display port).
You can hook up at least 4 without adapters (6 is the limit).
This card is somewhat overkill for ordinary BD playback, it is a highly capable GPU compute card. I use it for the MadVR GPU based renderer and SVP , a motion compensated frame rate converter based on OpenCL. Render times are almost 2X faster than the GTX680 I had before.