That seems pretty unlikely. The Mac OS X core operating system Darwin is also based off FreeBSD, but there's a whole lot on top of the core OS that they don't have in common, so Mac programs are not very easily ported.

Darwin includes a separate kernel and binary image format.

The question is the Sony OS using regular ELFs and the FreeBSD kernel with modules, or did they replace it entirely as well.

They used ELF (or actually SELF, Signed ELF) for PlayStation 3.

Correct. A SELF file is just an ELF-ish header with crypto abilities that wraps a normal ELF file. Many fields are duplicated... some are checked for validity while a different copy is actually used! ;-)

http://ps3devwiki.com/wiki/SELF_File_Format_and_Decryption

I'd say chances are pretty slim. They are only using the FreeBSD kernel. It's the stuff on top (graphics libraries, input handling) that really matters.

not strictly the FreeBSD kernel but the rather the BSD emulation layer ( which is quite a significant chunk of xnu ) on top of the Mach "microkernel" ( which until Mach 2.5 still ran in the kernel - Mach 3.0 moved the BSD emulation out to userspace). the "BSD emulation" started with 4.3 BSD and kept in sync with its successors but seems to have diverged quite a bit lately.

If someone wanted to build a PS4 ABI, much like how Wine works, there's a small chance that you could - but most likely not.