Typically, yes. Bring your own controller. Can't speak for "etc." but the rules are typically Normal Health, 3 rounds, unfiltered random stage select, first to two, double-elimination, character lock on win.
^all of that. as well as if you can't bring your own controller, you can find someone to share with. most people are cool enough to let you hold onto their's for a match, but before you give it back, make sure you disconnect the controller from the system. dojo is also banned in tournaments. be sure to let your opponent know if you want to button check, change character, etc.