Thank you for your interest on the upgrade. Normally we do recommend to contact the OEM manufacturer of the system. This is because they have run test and will be better suited to answer your questions.
But yes the processor is capable to run a 64-bit OS (http://ark.intel.com/products/31728/Intel-Core2-Duo-Processor-T7250-2M-Cache-2_00-GHz-800-MHz-FSB).
But I will again recommend you to check with the manufacturer of your system for drivers for the windows you will be installing.