Yes a 560 ti would handle Grand theft auto 4. But don't expect your computer to handle any future games very well. Athlon is a dieing series of CPU's and Phenom II is aging slowly. But a 560 ti would be perfect for GTA 4. at that retolution.
I think you are severely overestimating the athlon II. its a dual core with no L3 cache.
Both GTA4 and BF3 are CPU hogs that require lots of cores and lots of cache. I was completely unable to run GTA4 on my old Phenom dual core, that was heavily overclocked and it has L3 cache.