Yes. A 300w PSU can handle a Radeon HD 7750. HP PSUs are decent enough for the task. The Radeon HD 7750 only consumes 43w at peak power.
PSU is a Lite On Technology, rated standard Efficiency DC output +12va....12.0A and +12vb....16.0A Good for 300w if temperature does not get above 77 degrees, then wattage starts to drop above that, don't know total wattage that system may use.