Yeah it will run BC2, but I highly recommend going for the i5 2500k.
BC2 uses a lot of CPU power aswell as GPU so the extra CPU performance WILL improve the performance of the game.
This build is perfect:
Intel Core i5-2500K 3.30GHz (Sandybridge) Socket LGA1155 Processor - OEM £161.99
Sapphire ATI Radeon HD 5850 Extreme 1024MB GDDR5 PCI-Express Graphics Card **OcUK Exclusive** £114.98
Gigabyte P67A-UD3-B3 Intel P67 Chipset (Socket 1155) DDR3 Motherboard - (Sandybridge) ** B3 REVISION ** £104.98
Antec 100 One Hundred Ultimate Gaming Case - Black Antec 100 One Hundred Ultimate Gaming Case - Black £43.99
BeQuiet Pure Power L7 530W Power Supply £42.98
OCZ Platinum 4GB (2x2GB) DDR3 PC3-12800C9 1600MHz Ultra Low Voltage Dual Channel Kit (OCZ3P1600C9ELV4GK) £36.98
Sub Total : £421.59
Shipping cost assumes delivery to UK Mainland with:
DPD Next Day Parcel
(This can be changed during checkout) Shipping : £12.50
VAT is being charged at 20.00% VAT : £86.82
Total : £520.91
I have the same CPU and PSU and they're great. Plus overclocking is dead easy, literally just change a few numbers in the BIOS and away you go with up to 1Ghz extra juice.
The 5850 graphics card is roughly about the same as a GTX 460 so it'll run BC2 perfectly fine and if you ever want to get more power you can get another 5850 and crossfire.
That build is very similiar to mine and I'm really happy with mine