Therefore, vice-versa if you transfer you can purchase a Playstation 3 version (again) and apply it to your account, so yes it does.* Users who wish to play on both the PlayStation®3 and PlayStation®4 must purchase a separate copy of FINAL FANTASY XIV: A Realm Reborn for the PlayStation®4.
UNLESS Square Enix are setting it up so you can NEVER add a PS3 service account (which I doubt)