At a reasonable resolution (1920*1080 for example), with AA and AF, not a chance. On the same note the 560 wont max things out and provide playable fps either. If we look at the witcher 2 for example, max it with ubersampling and it's just about playable on a slightly OC'd 580 (1920*1080).
Maxing games requires expensive state of the art hardware, it's not something that a upper-mid level card can do, let alone one from a previous generation. However, the question remains whether you really want to max games out in such a manner? If you're a bit more casual about graphics and computing, as it sounds you might be, there isn't too great a reason for you to have a high-end card and max everything. Just get a good value card.