[wladimir]

It's an insurmountable obstacle, unless you plan on independently generating your own replacement headers (which is possible, but is going to be a world of pain).

How is it unsurmountable? I remember mingw/cygwin doing a similar thing for Windows.

[nupark]

It's not too hard to cobble together open-source headers and autogenerated minimally viable headers for the OS frameworks (this is what the initial non-official iPhone toolchains did).

They'll be very incomplete, however, quite a bit of software will not build correctly, and it will take a significant effort to clean them up.