with the nikon software* and c1 looking at the destination folder you can.
*camera control pro2? is that what it's called? we did this yesterday, the top lcd on the d800 flickers but it worked o.k with just one restart during the days shooting. annoyingly you can't live view on the camera but only on the computer screen while tethered this way. the preview in c1 doesn't update to the next shot so you haveto click on the next shot.
there were instructions on the web where you have to move files around in the library/terminal. you do not have to do this to get it to work.
we just used a 30 day trial of the nikon softwareand hope that C1 bring out a new d800/5dIII tethering version soon.
i have been using EOS utility in a similar way with the 5dIII/C1 only the canon software is free