Square doesn't mind how many consoles you install on, you can only log on with your ID on one system.
Everything I've ever heard about FFXI and PS3 has said that it doesn't work and never will. My bro plays FFXI all day everyday. He played the PS2 version for a year or so before upgrading to a 360.
If you're a fan of the game at all, you should get a 360 to play it over the PS2 version. Aside from the visual and text upgrades, only the 360 version has voice chat.