Would this lens fit a nikon d600?

Http://www.ebay.com/itm/281100861791

Of course, but you will have to manually focus the lens using the electronic rangefinder in the camera.

ANY AF, AF-I, AF-S or manual focus AI lens will work on the D600

I use a Nikkor 50 mm f/1.8 AI lens on my D3, D800 and D300