Will a low profile Amd 6670 work with my

You'd be better off going with a low profile 7750. More powerful card, but uses less watts.

Both 6670 and 7750 will work with a 220W power supply as long as the rest of the system is not using much power. I personally have a 7750 running on a 150W power supply in an ITX case with an i3-3220. It draws about 110W during gaming. Your AMD set up will draw a bit more power though.