Yes, Yes. Yes. I have a D90 with a 18-105 and got the D600. I have no regrets. I do think the 18-200 is a tad sharper.
I can now shoot at ISO 800 without hesitation. It focuses faster especially in low light, exposure is better (less tweaking or second guessing), and image quality is superior (especially colors and noise). You can see it clearly in 1:1 comparisons.
The D600 will feel right at home in the hand. Most everything is in the same place.