The active shutter based 3D monitors are great for 2D, because they can
support 120Hz - 60Hz for each eye in 3D, or 120Hz for regular mode. Your
GTX680 should easily handle 120Hz gaming and the difference should be
noticeable.
I think you'll have to make the new monitor, the primary one, if you
want games to open there. I am not sure though.
The monitor you listed is 3DVision compatible but you will need to buy a
separate 3DVision2 kit from nVidia (which normally has a pair of active
shutter glasses, and an IR emitter) Some monitors come with internal
emitters and glasses, and so you just need to buy 3DVision software from
nVidia, instead of the whole hardware kit.
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Noman