For Crysis on High at 1680x1050 with the eye candy you'll find even an 8800GT will struggle but should stick around the 25-30fps mark depending on the amount of action going on.
The computer you've posted isn't one I'd recommend. The CPU is a great CPU, I've currently got one but it only comes with 2GB of RAM and it's using a G31 chipset motherboard... that's like 2-3 generations old currently..
Also buying a prebuilt PC and then adding a graphics card to it isn't something I'd recommend. Considering the prices of the two items you've listed you're looking at spending around $800-$900?
Code:
$119.99 - Intel Core 2 Duo E7200 (2.53GHz/45nm/1066FSB/3M)
$107.99 - Gigabyte GA-EP45-DS3L (P45) Mainboard
$74.99 - 4GB Kit (2x2048MB) A-DATA PC6400 800MHz DDR2 RAM
$284.99 - Sapphire 512MB ATI/AMD HD4870
$84.99 - Western Digital 640GB SATAII 7200RPM 16MB HDD
$31.99 - Pioneer 215D Black SATA 20x Dual Layer DVDRW
$69.99 - Coolermaster Centurion 590 Midi-Tower ATX Case
$144.99 - Corsair HX-620W Modular ATX Power Supply Unit
Total $919.92
All prices are from Newegg.com
If you want to save money you can downgrade the HD4870 to an HD4850.
The CPU should be good to be overclocked to an easy 3.2GHz-3.4GHz, 4GB of RAM will see you running quite smoothly through Vista (if you have it) and 640GB should give you plenty of room to move. Case will accommodate the rig nicely and the HX-620 will be more than enough to even power two HD4870s in Crossfire (although for that you would need to have a Crossfire board :/)