Unfortunately, this doesn't have BF2 benchmarks. Some games take advantage of the 2GB, some don't. If anyone has BF2 benchmarks with using 1GB or 2GB, please post the site here.
Memory Benchmarks
These benchmarks use only 1GB of RAM. It doesn't explicitly say 1 or 2 GB, but when this article was written, 1GB was standard and that's what I'm assuming.
BF2 Benchmarks
I'm going to assume that the 6800 and 6800GS are very close in performance.
From the benchmarks, you can see that a better video card will get you better frames and that 1GB of RAM is fine. Depending on your resolution of your monitor and how much eye candy you want, BF2 can quickly make the 6800GS grovel.
Personally, if you have a PCI-Express slot then I highly recommend getting either the X1800XT or X1900XTX if you can afford the extra 80 bucks and wait for the MIR.