Easily. Hell, It even runs on old Dell workstation that I had lying around with 2x Pentium 3 1GHz , 1GB memory, 32MB Matrox 450 Video. Only could not find drivers for Network card so popped in another one I also had lying around and it works.
The PC will be powerful enough for sure (or else about 90% of the market won't be able to use it ). For hardware compatibility, you can always check the Windows 7 Upgrade Advisor.