Centrino is the platform, not the CPU. Any laptop with an Intel processor, chipset, and wireless card can be labeled Centrino. My Dell Latitude D830 is a Centrino laptop, with a Core 2 Duo T7500, Intel 965 chipset, and an Intel 4965AGN wireless card.
Your actual CPU is a Core 2 Duo T5250. The T9600 might work, but with differing bus speeds between the two processors, your laptop may not accept it. For best results, I'd recommend sticking with CPUs with the same bus speed, which in your laptop is 667 MHz.
Casey