NO. The FX6 doesn't qualify for RECOMMENDED for that gameplay.
REMEMBER: MINIMUM Means playing 1024x768 Low graphics and getting AT LEAST 15FPS
RECOMMENDED: Is the true 'gamer's experiance' as 'I saw on youtube'.
http://www.geforce.com/games-applications/pc-games/gran...
Recommended System Requirements
OS: Windows 8.1 64 Bit, Windows 8 64 Bit, Windows 7 64 Bit Service Pack 1
Processor: Intel Core i5 3470 @ 3.2GHZ (4 CPUs) / AMD X8 FX-8350 @ 4GHZ (8 CPUs)
Memory: 8GB
Video Card: NVIDIA GTX 660 2GB / AMD HD7870 2GB
Sound Card: 100% DirectX 10 compatible
HDD Space: 65GB
DVD Drive
Whenever you have a question about you can always check with www.canirunit.com and see how your hardware stacks up in any game. It doesn't matter if you believe your " PC can run the game at reccomended " if you don't have THAT hardware or better then you CAN NOT run it 1080P High+ and expect SMOOTH game play and 60FPS.
You could upgrade to a FX8 but even if you spend $1000 and got a i7EE edition with a 270X won't be enough to get out of the 30s
http://forums.anandtech.com/showthread.php?t=2428094 (note that is what they used the 270 with to get that score!).
If you don't have the $700+ for a normal PC Gaming rig, then take the $200-400 and instead get a PS4, it plays GTA V at 1080P 30FPS on HIGH settings.