Is it likely? Yes. All depends on how much it's customized. With XboX there were three main problems with emulation
1. The processor was MODIFIED, it was a custom Pentium 3. But it was close enough where a recompiler could easily handle it with not much dip in performance
2. The graphics was an nVidia card and the API was Direct X. However, it used a heavily modified Direct X code that was never used in any version of Windows. From what I remember with cxbx a few years back, that was the main problem because ALL graphic calls had to be modified.
3. The system. From that generation of consoles the games no longer run 'bare bones' on the console and interact with hardware directly, but they use the system to handle everything. And while XboX's OS was based on Windows NT kernel, but that's all the similarities.
Now, let's put this in comparison to PS4
1. The processor is kinda unknown, I can't find anthing specific on how much it's customized. So, it may be normal X86, in which case all low level instructions would be prime to go.
2. The graphics is AMD GCN based. And it supports Vulkan. However, how many of the games running on it are Vulkan based? It's unknown. All in all, video calls would need to be most likely 'translated' to either OpenGL or Direct X (in case of Windows), which brings us to
3. The operating system. Now this will be the biggest obstacle. PSP and PS3 make a HUGE use of the OS when rendering graphics, it's the reason why PPSSPP is a high level emulator, because everything the games do are system calls to graphic functions. Therefore, until someone manages to, so to speak, 'crack open the system' of PS4, a chance of an emulator are non-existent. Unless someone manages to port PS4 OS to work on a standard x86 PC, and good luck with that, it would be a driver (or rather, module?) mess.