Yes, it will run most games at low graphics/video settings. It is by no means a "gaming video card" and is really a low end, general purpose video card. Still, it will work. Just don't have huge expectations.
Honestly, I think the HD6670 is one of the best price/performance GPUs on the market. It is a surprisingly capable GPU for the money. I have used in several systems (as well as its HD6570 sibling) and have been VERY pleased with their performance.