I think it depends on how you bought it. If it was digital download and anything like Tera's installer, it might have downloaded the entire installation file set to a folder with a file system like: Data001.dat, Data002.dat, etc., In which case you can simply copy the install files to an Ext HDD and use them on the new OS install for a MUCH faster install.

If not, then you'll simply have to run the downloader again and re-download all of the files. Unfortunately, I seriously doubt you'll be able to simply copy the program files as typically with large scale MMO's like this, and the many mini-patches the game has already released, there are typically ALOT of files that link to Registry Keys that need to be configured properly (This happens during the installation of the game), and if you simply copy the program files, the registry will still be new and therefor un-optimized or rather unconfigured for the game's requirements.

Some major MMO's like Blizzard's World of Warcraft and other titles have the ability to run from an external source and the source can be moved from OS to OS without any problem but Final Fantasy XIV, to my knowledge is NOT one of those types of game software.

Is it worth a shot? Yes. Is it going to work? My probability points towards No.