no it will run on high ish settings but not max the 6670 is a low end card you need a mid range card to max out crysis and get 30 fps minimum. your system is fine for it on the whole just a little weak on the gfx. for 650 its a very nice build. maybe in a few months you can upgrade that gfx and move from low mid to high end. a small tweak here and there and you will have a very nice pc.
also your hdd is poor. you will get a lot of texture pop because its slooooow much better to get a 7200rpm 1 or get 2 and run them in raid 0.
even if you get 2 500gig 1s you will get much smoother gameplay and system experience.
i run 2 of my 3 1tb spinpoint f3's and get an average of 180MBps read and write. which is over double what yours will top out at... it really is a good investment if you dont want to get a ssd that costs way to much for the storage you get...
(reason i say this is some manufacturers have just cut production because ssd prices were coming down to fast, they basically are holding the price up which is unfair to the end user)