Using a cocoa command line application in Linux-Collection of common programming errors
No, you cannot run a program that was compiled on and for a Mac on a Linux system. So you will have to compile it for (and on) Linux. Apple’s Foundation framework is not available for Linux, but have a look at GNUstep, a free and open Cocoa implementation.
I don’t know if GNUstep can read archives that have been archived with Cocoa’s NSKeyedArchiver, though.