It's not in FFXI soundtrack or any of the add-on soundtracks, at least.
I forgot to mention, FFIII also has the Final Fantasy theme play in the end. It's very short and only has the first few notes, but it's definitely there, in both the NES version and the DS version. It's in the song called "Everlasting World", and a full version of it can be heard in the track Rebirth on FFIII: Eternal Legend of the Wind album.