The minimum system requirement but with a good GPU, will it blend?

As all the slots on my current PC are full and I have a GTX 780 Ti lying around and would like to use it for GPU cycles render. I would just do odd numbered frames kinda 2d PC farm setup. I was going to buy a PC as far as the minimum system requirements for Blender like an i3 with 2GB of ram with a couple of PCIEx16 slots kinda cheap machine.

But I’m not sure if the low end would slow down the GPU render time.

Is the Ram and CPU the least important part of the machine when GPU rendering? As long as it can run Blender within system requirement, right?