Not as an "ordinary" processor or RAM, no.
Dedicated video RAM is not in the same physical address space as your regular RAM and so cannot be directly accessed by your processor.
As for the GPU, the GPU doesn't execute the same instruction set as your CPU (if it did it wouldn't be a particularly fast GPU), so code from ordinary programs can't run on it. As Ramhound indicated there are programs that make specific system calls that take advantage of your GPU; there are even programs (typically things like video editors, CGI renderers, etc.) that supply their own code to run on the GPU. But each program has to be specially coded to do that. If the program supplies its own code for the GPU this has to be different for each GPU family - for example, the code that exploits nVidia's PhysX won't run on AMD GPUs.