It depends on the game that you will be running, the detail settings in the game, resolution (you would probably want to run it at native resolution, so 1366 x 768), and anti-aliasing (removes jagged edges). If you mean modern AAA titles, then it will not, you would have to spend a lot more on a laptop. If you want to run older games or less graphically intensive games, you might be able to run it at 60 fps.
60 fps is an unrealistic expectation for a laptop with those specs. But that does not mean that the game is unplayable (Consoles usually have games capped at 30 fps to give you an idea on smoothness). Try to get a laptop with a dedicated graphics card and try checking out benchmarks on various websites for the games that you want to run (ex: Tom's Hardware, Anandtech).
You may even want to consider a Llano based AMD processor (significantly better than Intel's HD 4000 integrated graphics) if a laptop with dedicated graphics is too expensive. If you are really on a tight budget, I might suggest a desktop over a laptop. If you choose to go the desktop route, do NOT buy from major desktop brands.
Get it locally built, or build it yourself. You will get a PC that is optimized for gaming (better graphics card) for a lot less. There are some great $500 value gaming desktops, but please don't expect to be running every game at max settings at 1080p at playable frame rates.
You can't get a decent gaming laptop under $400. Gaming laptops use high end equipment, and are expensive for a reason.
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