No. When you change the operating system, you change a huge amount of things, like how memory is stored, and just in general how system calls are made that screw up any executable that's run. The mac version is no different than the windows version in terms of Linux really. When I say it'll run, I'm checking if it'll run on Wine, which lets windows programs run on windows (though buggily, that's why some games don't work, they just crash).
To check to see if smoehting'll run, just check here:
http://appdb.winehq.org/
Just search your application name. If it's platinum, it means it runs perfectly or near-perfectly. Gold is runs well enough. Silver means it has some major bugs. Bronze means it's almost usable, and garbage, is well, you know, garbage