Not near max settings for that price. A decent gpu and cpu will be 400 alone that can run games maxed, let alone motherboard, case, monitor, harddrive, power supply, mouse, keyboard. The build will usually end up closer to 800+.
Actually you can, in fact a friend of mine just set up a gaming rig for about $550 that maxes out The Witcher 2, Skyrim, Batman Arkham city, Crysis 2, Sleeping Dogs and others.
Here's quick YouTube search on "budget gaming pcs", it includes gpu/cpu/case/mobo/power supply/ram/hd for 423 dollars and in the video it maxes Sleeping dogs (with the high resolution texture pack), Dirt 3, Batman: Arkham City at full HD at 1920 x 1080 and in DX11 at fully playable FPS, there are many of them on there that show 400-500 dollar PC's maxing out most games. Mouse/keyboard is like 25 dollars? A monitor will be 100 bucks or so, but most people already have decent monitors.