Perhaps but once again, as the D700 did with the D3, it could cannibalise D4 sales without a real need to do so, given the 5D3's pricing.
The hypothetical D600 would quote clearly be completely different camera to the professional top end sports and PJ camera that is the D4.
It might possible eat into the D800 sales, people with marginal finances will take a lower end D600 rather than stumping up for the D800. But again, these will be different cameras and the D800 sensor alone will differentiate the 2.
The lost D800 sales would more than likely be recouped by people who can now afford to buy a new FX body, people who were thinking of spending $1200 on a D7000 (or replacement) or a DX D400. And if a DX user is persuaded to upgrade to FX then they will buy some more FX glass.
There are probably also people out there looking to move into an entry level Full frame camera, where Canon provided a 5D classic second hand and 5DMKII with the same IQ as the 5DMKIII. Providing a cheap Nikon FX camera will make some people swing to a Nikon D600 which could offer better IQ and definitely better AF than the 5DMKi and MKII.
It is also a bit of a myth that the D700 had a large affect on D3 sales, mostly spread by Canon users to justify why their 5DMKII was crippled. People that needed a top end professional camera still purchased a D3, and the D700 generated plenty of sales from people who could not afford a D3. Perhaps some pros who needed a backup body to go with their D3 purchased a D700 instead of a 2nd D3, but then others would buy a D3x to go with a D3. You got to consider the price difference between a D3 and a D700 to a pro was not that big, and professionals tend not to worry about differences in prices but in the quality of the equipment. Anyway, with the release of the D3s there was a clear differentiator, about 1.5 stops low light performance.