It's not really "supported" if you are feature limited by using it. The game doesn't offer the ability to change your movement speed unless you're using analog controls, which is only possible via the thumbsticks. Arcade sticks are purely digital input.
I still played the first week with an arcade stick out of pride, lol

But analogue is waaaay better, yep.
Also, 11th place on Challenging Story mode leaderboard. Hell yeah!