Yes, you definitely can. Many players feel like SE is more in favor of players using the gamepad rather than the keyboard (if nothing else, they don't seem to like letting PC players use the mouse :/ ). I'd use a 360 controller myself if it wasn't such a pain to put it down every time you need to talk.
I read about this issue that doesn't allow to play FFXIV with a PS3 controller on Windows 7, but since PS3 and PS2 controller are almost identical, will it work the same If I just plug in a PS2 one? I played FFXI with it, although I was on PC, and I never had a complaint. Thanks If anyone knows.