leaks happen, encryption gets broken, digital signatures get faked.
look at the PSP, it's practically open-source at this point.
given that people are releasing homebrew for PS4, it hints that all the tools required to do such a thing are currently out there in the wild.
i'm pretty sure it's possible.
HOWEVER!
the libraries we depend on (ie: SDL) aren't available in PS4 flavour. given that they're open-source as well, it might be possible to compile them for PS4, but you'd have to add PS4 support to it manually.
so i'd consider that the major hurdle, and the thing you'd want a bounty on: SDL
if you can get a PS4 compatible version of SDL, you gain access to a wealth of games almost inherently.