Yes, it will run on a GeForce 6600. But it will be pretty slow. Max frame rate probably won't be above 15 FPS and it will slow down to a slide show occasionally. I haven't measured the frame rate with anything like Fraps.
How do I know? I have a machine here with one of these cards in it. It's in a box with a 2.8Ghz P4 and 1GB of PC3200 RAM on an Intel D865PERL motherboard with a Maxtor 120GB 7200 RPM hard drive with 8MB cache and a Pioneer DVR-109 DVD/CD drive. The machine is running Windows XP SP2.
You can get a 512MB GeForce 7600GS AGP8X video card for less than $200. And one with 256MB for about $100. This will significantly improve your framerate and make the at least playable.
AGP is a dead-end, though. I think I'd wait until you can buy/build a new machine with PCI-Express. All the new video cards are PCI-E only, I think. By next year (early 2008), the prices on cards like the 7950GX2 (or equivalent ATI card) should have come down from ridiculous to merely outrageous.

I built a new machine late last year so I could get on the PCI-E (and LGA775) bus. I started off with mid-grade on the video card (GeForce 7600GS PCI-E) and low end on the CPU (3.2Ghz P4).
I don't believe that going from AGP to PCI-Express has made any difference in my game playing experience. The new machine is faster than my old machine but I think that's just because the CPU is faster (2.8Ghz -> 3.2Ghz), the memory is faster (DDR-400 -> DDR2->800), and the CPU clock is faster (533Mhz -> 1066Mhz).
Both machines have GeForce 7600GS/512 video cards. One is AGP8X and the other is PCI-Express.
Both machines have 1GB of RAM.
The difference in game performance is noticable. But not significant. The new box still chugs on R6Vegas. Both machines play GRAW okay.
Hope that helps.
