Will the XFX GeForce 9800 GT 256-bit GDDR3 work on my current system specs?

[Everlong]

It won't kill your PSU. It either won't startup, or it will startup and when you begin to run a program such as a game, your PC will just shut down automatically.

You could maybe get away with the smaller 9600. It only uses 59 watts and needs 300w minimum PSU.

Newegg.com - ASUS EN9600GT/DI/512MD3 GeForce 9600 GT 512MB 256-bit GDDR3 PCI Express 2.0 x16 HDCP Ready SLI Supported Video Card - Desktop Graphics / Video Cards

There's two versions of the 9600, this one is the 59 watt version as it has the 600MHz core speed and 1500MHz memory speed. If you were to go for the 92 watt version of the card, which has 650MHz core speed, and 1625MHz memory speed, you'd need a 400 watt PSU.

Though your current processor is going to hold back any of the cards mentioned here.