Will your Cougar 650W power supply hold up if you were to add a Radeon HD 7870? Yes, most definitely. Most people think that because their system has a 650W power supply, that you would use close to that with a video card installed - but in the real world, most systems don't even get close.
What that type of system, in a stressful game such as Battlefield 3, I'd be surprised to see you pushing past 200-250W of actual power consumption. You could even stretch out to the HD 7950 or 7970 and still find you'll have enough juice left to spare. The new 28nm-based GPUs are incredibly power efficient, as are the new CPUs that have arrived over the last 6-18 months.
Your 650W PSU will hold up, for sure - now go out and get the HD 7870!