Not really some may be nearly playable in the lowest resolution and settings but you really want at least a radeon 6670 as a minimum for gaming. If you must get one you mentioned the 6450 is alot better but don't expect a good gaming experience.
No those are not considered gaming cards. They are more like multimedia cards. Far Cry 3 and BF3 both have pretty high requirements. The Radeon HD 6670 is probably the best video card you can buy for under $65 that will give you decent performance if you were to play @ 1920x1080 resolution and low graphic settings. The Radeon HD 7750 is the best graphics card for under $100 that can give you decent performance at 1920x1080 resolution with medium graphic settings.
The lower the resolution, the higher you can potentially set the graphics quality to.