It is? Test it with a low-end 5400 RPM UDMA33 hdd like the PS2 one and then an SSD and you'll clearly notice the difference.
Altough of course it's small, tbh it's barely noticeable (I have FFXI on my SSD and on my Caviar Black as well), but it's there.
There's a bigger difference with connection speed, the quality of your connection. You can easily test it by connecting with a low-end GPRS/EDGE/PSTN connection and then comparing it to a high quality cable line like those available in some countries.
There's also another difference in the overall latency if you play FFXI at your place or in Japan.
Have you ever been in Sekigahara? There are bars there where you can play FFXI for free. Have you ever noticed the huge difference there is when you use a JA and when the JA really goes off in the screen? When you interact with an NPC and the options are loaded up, when you zone and the time it takes for the items in your inventory to load up, the time it takes to sell/buy items from an npc, the time it takes to move an item from your inventory to your mog house.
There's a very noticeable difference and if you've been there and tested it you would know what I'm talking of.
Of course I'm not saying there is something exagerated like, say, 5 seconds difference lol, it's very small! But at the same time it's also clearly noticeable and I think it has a big impact when you play this game 4+hrs a day.