Yes you can. It doesn't even have to the be the same folder, the game will run from anywhere, even a USB flash drive, as long as you keep the structure the same and just start it by using ffxivboot.exe in the boot directory.

Make sure you also move the folders in your Documents though:

Documents\My Games\FINAL FANTASY XIV - A Realm Reborn

That folder contains all your hotbar settings, gearsets, etc. That one has to go back in the same place.