What resolution will you be on? You should be able to run it since the min VGA is a 7800GT but how smooth it is will really depend on your resolution.
On the UK BC2 forum there is a huge performance thread you may want to look through. Look at this guy's setup at 1024x768:
FPS: As defense(min 57 max 109 avg 84),Attack(min 65 max 109 avg 85)
OS: XP Pro
CPU: AMD Phenom 2 BE 955
Mobo: Gigabyte MA785GMT-US2H
PSU: 650 Antec EarthWatt
Hard Drive: 1 ide 120gb for os + 1 sata 320gb for games
Soundcard: Audigy 2
Performance Description: taken with default medium settings at 1024x768, fraps recorded for first 1min on each side, didnt do a full re-install after updating hardware so i wouldn't be surprised if there is some fps loss as a result.
OS: Win xp 32 sp3
CPU: Intel Core2Duo E6750 @ 2.66ghz (stock cooling and speeds)
CPU Temp/s: normal ~40
GPU: EVGA 8800GT (stock cooling and speeds)
GPU Temp/s: normal ~60
Memory/RAM: 2x2GB DDR3 1600
Mobo: Gigabyte P35
PSU: CoolerMaster 900w
Hard Drive: Seagate Barracuda 75gb
Soundcard: Mobo sound - Realtek HD audio 5.1
saw an enormous performance boost with last patch on my dual core.
went from almost unplayable in LOW, to running like gravy in HIGH.
AAx1 (I can't change it, there is no option other than 1 and changing the setting in the options file seems to have no effect)
AAx16, set to DX9 in options.ini.