Unless you're coding an emulator or using an IPS patch, it doesn't really make a difference whether or not your ROM has a header. The only reason it matters with IPS patches is because the data gets shifted depending on which ROM was used. Most people just happen to use a headered ROM for FF3us when making IPS patches.
From what I understand, headers are, or were, necessary for dumping ROMs directly from the cartridges, but emulators don't need them to run the game.
One other thing to note is that ROMs labeled with [!] typically do not have a header, while those without the ! typically do.