Yes it should work fine on both counts.
The GF6600 would act as primary and games would usually black out your PCI screen unless they support spanning etc. You could change the boot sequence and assignment of the cards through the bios, and force recognition through a regedit, but unless you need to let M$ and nView manage the cards.
I did this with my old AIW PCI and the R9600P, and while I know that that's ATi and this is nV, M$ doesn't care to much unless you want to do something special, like spanning, etc.
For any special tweaking use UltrMon, but otherwise nView should be fine. You may have DVD playback issues, but that's the usual Macrovision, DRM crap everything has to deal with, in which case you need to adjust your overlay features. I forget what it looks like in nView.
Anywhoo, should work without major issue. The only major problems I've heard about is coming back from gaming sometimes the second montior may hang, and that's usually a driver glitch, but common.