Well I installed my 7800GTX on the weekend, and just tried to run BF2. I have it patched to the latest version (1.21).
I managed to get to the level load screen, but then it got stuck at 62%, and when I pressed escape it spent three minutes claiming it was 'unloading resources' at which point I got bored and rebooted.
From my experience though, BF2 tends to black screen if you are cracking the game or had a no-cd crack on it before and have since patched it. But it's a very buggy game. I thought actually buying it would remove some of the bugs, but alas, not really.