You will need to recompile it at least, not because of the kernel, but because of the libraries. In all likelihood, it will take more to port a Mac OSX application to Linux than it would to port the Windows equivalent. The reason is that Mac OSX has many system calls that interoperate with its proprietary user interface - the Mac does not use X Windows. While the equivalent Windows calls have largely been rewritten for Linux (via WINE, over the last decade), the equivalent for Mac OSX does not exist.
Apple is very much a proprietary company, as is the software they produce. I like the Mac, and have owned several - but I have no illusions about their business.