I agree with both Apollo and Stormy. I believe the Pro can indeed display ED's graphics at 4K (checkerboard), but I also don't believe this is cut-and-dry for Frontier. If ED were a PS4 exclusive, then I think Frontier would have more 'motivation' to do all the incredibly clever optimizations needed to achieve this feat on a PS4 Pro. Being a cross-platform product that's primarily targeting the PC market, I doubt Frontier is going to invest in time and talent needed to make ED really shine on the PS4.
What's sad about this is listening to David Braben talk about how clever he was to get the original Elite to run on computers of those days. For example, redrawing the ship via XOR instead of erasing the screen to greatly increase framerates. We need a modern version of David for the PS4 version of ED. Unfortunately my experience with younger developers coming from PC programming is that they don't know how to optimize in this fashion, as they live in a world where you just throw more CPU, GPU, and RAM at performance problems instead of solving them with clever coding. Developers that make console exclusives are much better at this IMO.