I had the same thoughts regarding pixel pitch and hand held images. I would think that if you could do it with your D7000 you should be able to with the D800. I do notice for maximum sharpness I need to carefully watch my shutter speed.(with the D7000.. I don't own a D800)
Given higher pixel count of D800 some edge softness may be more apparent with FX glass but this wasn't really the jist of your question and probably only noticable with significant pixel peeping.
If you like a bigger camera I would go with the D800.
BTW I think the autofocus on the D600 is a little beter than with the D7000 and certainly not lacking, although the D800 is even better.
"Cameras and lenses are simply tools to place our unique vision on film. Concentrate on equipment and you'll take technically good photographs. Concentrate on seeing the light's magic colors and your images will stir the soul." Jack Dykinga