You can use both cards- just not in an SLI configuration.
An obvious example would be using your GTX 275 as the primary graphics renderer (i.e. as your graphics card) and use the 9600GT as a dedicated PPU (PhysX/Physics Processing unit). This would offload any gaming PhysX/Physics calculations to the 9600GT and allow the GTX 275 to render the core aspects of the game unencumbered by having to calculate the PhysX effects- *remember to enable the 9600GT in the nVidia control panel under the PhysX tab.
Assuming that your CPU and GTX275 aren't running massive overclocks and you have a fairly normal range of added componenty the TX650 should be adequate for the job.
The GTX 275 requires 2 x 6 pin PCIe power (theoretical max power 75w through the slot plus 75w via each PCIe 6 pin = 225w. TechPowerUp list
220w maximum in testing), the 9600GT has 1 x 6 pin PCIe mainly because it sits on the threshhold of the PCI-E slots power delivery. TechPowerUp's convenient chart lists max draw at 78w, which as a dedicated PPU it would not approach.
So......225w + 78w = 303w / 12 = 25.25 amps required (Your PSU is rated at 52). Factoring in your CPU, harddrives, powered peripherals, board, fans etc. you are still well within limits.
Sorry about the mega-detailed answer but rather than just answer "yes" I thought it best to explain the process behind it.