Will PlanetSide 2 run on this PC?

I would go ahead and say no, only because you don't have a dedicated video card, and you have less than the minimum requirements of RAM for the game to run.
minimum requirements for the game:
CPU: Intel Core 2 Duo E6850 or higher / AMD Phenom II X2 or higher
RAM: 4 GB
OS: Windows XP
Video Card: nVidia GeForce 8600 series or higher / AMD or ATI 4850 series or higher
Sound Card: Yes
Free Disk Space: 15 GB

Recommended Specs for the game:
CPU: Intel i5 processor or higher / AMD Phenom II X6 or higher
RAM: 8 GB
OS: Windows 7
Video Card: nVidia GeForce 500 series or higher / AMD HD 6870 or higher
Sound Card: Yes
Free Disk Space: 15 GB

your system Specs:
System Manufacturer/Model Number HP ProBook 4530s
OS Windows 7 Home Premium 64 Bit
CPU intel core i3 @ 2.1 Ghz
Memory 2.00GB
Graphics Card Intel HD Graphics family 799 MB
Monitor(s) Displays Generic PnP monitor
Screen Resolution 1366 x 768 (32-bit) (60 Hz)

Keyboard Integreted Keyboard - KBC Version 22.1A
Mouse Logitech Wireless Mouse
Case Is that really necessary?
Hard Drives OCZ SSD Hard Disk 150 GB
Internet Speed Ping: 26ms Download: 31.66 Mbps Upload: 1.95 Mbps

And to answer the question about making a game run better without turning down its settings, i personally use Razer Game Booster. Basicly it forces your system to devote more resources to the game by shutting down certain background processes and disabling services that are not system critical while a game is running.