Generally speaking, I do not recommend it.
When running a Radeon HD 6670 on any PC regardless of the CPU, I generally recommend at least a good quality 300w PSU. You can probably run it, but you will be pushing a 250w PSU near it's limit on the +12v rail. The harder to push it the sooner the PSU will fail.
If I am not mistaken, nearly all 250w PSU (whether good or bad quality) provided roughly 14 amps on the 12v rail or 168w of power; 16 amps at most (192w). Under load a HD 6670 draws about 65w, a Core i5-2500 draws about 65w, the typical hard drive draws and optical about 17w each. All fans roughly 12w.
Assuming one hard drive, one optical drive and two fans you are looking at 188w, that's excluding any spike in power draw that can take place under normal conditions. The power draw from your proposed system is either borderline limit or beyond the limit of a 250w PSU.
I typically stay from using Outervision (above link) because I typically find that their "estimates" were way off actual measured power consumption done by reputable sites and other research I have done. However, that was back in 2008, perhaps they have changed their ways, but perhaps not.