In some modern games, yes. Shouldn't be too bad though, you can crank the graphics settings up to max the card out.
If you can upgrade the CPU later then you'll be fine. Basically you might see low minimum FPS compared to a good CPU, but either way a 560 is a nice card and you should be able to turn graphic settings up nicely to put full load on it.
You will be able to play every game with good avarage and max fps but your minimum fps will be very low in some situations.
Basicly Avarage frame rates are more dependent on the GPU while minimums are more dependent on the CPU.And a High-End card like the 560Ti is usually matched up with a proccesor twice as fast as yours.
He said the 560 not 560 Ti, and the 560 would play BF3 at medium on a 1080p display, with a few options up at High. The CPU however would definitely bottleneck that game in multiplayer, causing some bad lag at times. In single player it will do fine.