NO.
-ARMA 2 is poorly optimized and runs poorly on even high end hardware.
-BF3 will play on that hardware, I've seen it on a system like that before, but at low settings and low resolution.
You need to save up and upgrade, 700-800 will get you a system that can play BF3 well.
I would advise against using a weak card like a 7750 in BF3 as the above poster mentioned. You won't be able to pay the game well at all on that card. BF3 is much more demanding in multi-player when there is over 30+ people, it will cripple you. (Single player BF3 will perform nothing like multi-player)
Get an ASUS GTX760 with a cheap AMD based build, it's 250$ dollars for the graphics card and will handle BF3 on ULTRA/60+FPS.
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
CPU: AMD FX-8320 3.5GHz 8-Core Processor ($153.61 @ Amazon)
Motherboard: Asus M5A97 R2.0 ATX AM3+ Motherboard ($87.99 @ Amazon)
Memory: G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory ($64.80 @ Newegg)
Storage: Western Digital Caviar Black 1TB 3.5" 7200RPM Internal Hard Drive ($89.99 @ Newegg)
Video Card: Asus GeForce GTX 760 2GB Video Card ($250.98 @ SuperBiiz)
Case: Cooler Master HAF 912 ATX Mid Tower Case ($49.99 @ Newegg)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($44.99 @ NCIX US)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.98 @ Outlet PC)
Total: $739.33
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-09-19 02:59 EDT-0400)
This is a cheap build that will handle BF3 easily, and should be able to handle BF4 fine too.