Yes it will run. However keep in mind you'll be severly bottlenecked by your CPU. I would say get something like a 5670: http://www.newegg.com/Product/Product.aspx?Item=N82E16814161334
and save the rest. In games like BF3 you'll experience annoying micro-stutter because the CPU can't keep up with the GPU. As one who's been in a situation similar to yours a while back, I can say it's a good idea to keep balance.
That said, you could get the 7750 and use it for later if you want to upgrade. 7750 is a decent card there's no doubt about that.