Its difficult to say with certainty, as it seems to depend on the chipset the controller uses inside.
For example, I have one of these:
http://uk.ign.com/articles/2009/01/28/mad-catz-fightstick-review

The Raspberry Pi just didnt want to know, so I bought something very similar to this:
http://www.ebay.co.uk/itm/NO-Delay-USB-Encoder-PC-to-joystick-for-Arcade-Mame-5Pin-SANWA-Push-buttons-/191775734565

and had it fitted in the arcade stick and I was away. No problems at all.

This forum may know more about the compatibility:
http://forums.shoryuken.com/

If you want to splash out more cash you could get one of these: