It would 'run' for sure! The 295 is a very powerful card. Even the 280 for that matter is a very good card. Assuming you have a decent CPU, you should manage BF3 just fine.
Just keep in mind that you won't be able to take advantage of the DX11 features of the game since the 200 series don't support DX11.
Oh yes im fully aware of DX11 features that these cards doesn't support , Ive got gtx295 and QX9650 cpu running at 3.7Ghz , i do get between 55-75 fps in Bad company 2 with 4aa maxed out at 1920x1080 , the 280 series drivers raised the performance pretty high comparing with the older drivers when this card was valid in benchmarking a year ago . man its running faster than GTX480 , only downside its the fact that it is dx10 only .