Will this work

Solution
Just a little bit more, but worth it. That Coolermaster power supply has disaster written all over it, to be avoided at all costs, substituted a slightly more expensive but completely reliable PSU. Upgraded your RAM to 1600, and substituted an ASUS motherboard similar in price to what you had selected before but it's a better board (just don't try to overclock with motherboards in this price range)

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($112.99 @ NCIX US)
Motherboard: Asus M5A78L-M LX PLUS Micro ATX AM3+ Motherboard ($44.99 @ Micro Center)
Memory: Kingston HyperX 8GB (2 x 4GB) DDR3-1600 Memory ($74.96 @ Amazon)...
Just a little bit more, but worth it. That Coolermaster power supply has disaster written all over it, to be avoided at all costs, substituted a slightly more expensive but completely reliable PSU. Upgraded your RAM to 1600, and substituted an ASUS motherboard similar in price to what you had selected before but it's a better board (just don't try to overclock with motherboards in this price range)

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($112.99 @ NCIX US)
Motherboard: Asus M5A78L-M LX PLUS Micro ATX AM3+ Motherboard ($44.99 @ Micro Center)
Memory: Kingston HyperX 8GB (2 x 4GB) DDR3-1600 Memory ($74.96 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($51.99 @ Amazon)
Video Card: Sapphire Radeon R9 270X 2GB Dual-X Video Card ($189.99 @ TigerDirect)
Case: Aerocool Strike-X One ATX Mid Tower Case ($33.00 @ Amazon)
Power Supply: SeaSonic S12II 520W 80+ Bronze Certified ATX Power Supply ($65.98 @ SuperBiiz)
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer ($15.99 @ NCIX US)
Operating System: Microsoft Windows 8.1 (32/64-bit) ($94.99 @ NCIX US)
Monitor: Samsung NC190-1 19.0" Monitor ($74.99 @ Amazon)
Wireless Network Adapter: Belkin F9L1001 802.11b/g/n USB 2.0 Wi-Fi Adapter ($9.00 @ Amazon)
Total: $768.87
Prices include shipping, taxes, and discounts when available

Not a bad build though. That monitor is really low end, but if that is your budget, that is your budget. For about $110 you can get a nice 23" 1080p monitor with 60Hz refresh and 5ms response, much better for gaming if you can swing the extra 35$ it would make a huge difference in your gaming experience. 🙂
 
Solution
Here's a revised one with that monitor I was talking about, slightly less expensive PSU, but it is decent. Total $40 more expensive than your original build, but that monitor is going to be massively better than that 19"

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($112.99 @ NCIX US)
Motherboard: Asus M5A78L-M LX PLUS Micro ATX AM3+ Motherboard ($44.99 @ Micro Center)
Memory: Kingston HyperX 8GB (2 x 4GB) DDR3-1600 Memory ($74.96 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($51.99 @ Amazon)
Video Card: Sapphire Radeon R9 270X 2GB Dual-X Video Card ($189.99 @ TigerDirect)
Case: Aerocool Strike-X One ATX Mid Tower Case ($33.00 @ Amazon)
Power Supply: Corsair CX 600W 80+ Bronze Certified Semi-Modular ATX Power Supply ($49.99 @ Newegg)
Optical Drive: Lite-On iHAS124-14 DVD/CD Writer ($15.99 @ NCIX US)
Operating System: Microsoft Windows 8.1 (32/64-bit) ($94.99 @ NCIX US)
Monitor: AOC E2360SD 60Hz 23.0" Monitor ($109.99 @ Amazon)
Wireless Network Adapter: Belkin F9L1001 802.11b/g/n USB 2.0 Wi-Fi Adapter ($9.00 @ Amazon)
Total: $787.88
Prices include shipping, taxes, and discounts when available

Good luck! :-D