Yes.
Game Editor 1.4.0 exports games without any problem to PC, Mac or Linux. On Mac, you have to make sure the exported file doesn't match any current file names on your desktop to export to, then to make it work after it's finished exporting to the desktop, enter in a new terminal window:
chmod +x Desktop/YOURGAMENAMEHERE
That one time command will change the desktop file's image to a black terminal box that you can then open the game on a Mac (and Linux if required for a Linux export) by double clicking, and for PC, just leave the file as a .exe file, which PC can open up without having to enter the chmod command. That creates a standalone game where GE is no longer required to run it.
Skydereign mentioned he's currently working on version 1.4.1, which will have the option to go fullscreen or windowed as the gamer's choice, which should be very welcome considering Unity has the option to go fullscreen or windowed, which is very useful for different screen ratios/sizes.
My first game, Tomb of Twelve, had so many tiles in it, that it exceeded the visible tiles the Game Editor Editor mode could handle, making many tiles invisible while in Game Mode in the Editor window, but as soon as I exported it, all the tiles were visible and present which was a huge relief after putting hundreds of hours into the giant project.