It depends what you are doing really. If you aren't doing many GPU bound tasks e.g. gaming, graphics editing etc. you won't get much more performance out of everyday computing tasks by simply adding a GPU aside from any applications that have been optimised to use CUDA/Compute cores.
But if you are looking into doing more GPU intensive stuff I would personally recommend a new PSU as 255W is fairly weak and you would only be looking into getting discrete graphics cards (GeForce 210 etc) which wouldn't be up to the task for gaming.
Bear in mind that you would likely be bottlenecking the GPU as well as motherboards that are compatible with most Core 2 series processors (Socket 775) are typically running on PCI-e 1.x so it would not be used it maximum potential but still functional.
Hope you found this helpful!