figure out the communication protocol of the xbox controller
build a patch cable that has a microcontroller that outputs the code for a random button press when its input is triggered by the controller with the same communication protocol
a ring counter whose clock is stopped and outputs enabled by the button push. If it is counting to 16 many times every second, then it will appear a random output is activated every time the button is pushed. The output can be sent by holding it in an SR latch, until the next button push changes the output again.
I would think a circuit to simulate a button being pressed, with a small knob to set the repetition rate would be more useful. My thumb used to get all kinds of sore when my kids made me play those games with them. If I could buy a controller that would 'bang rapidly' on the buttons, instead of using my thumb to do it, I'd buy it.
There was one offered by Gamestop that had a button repeat function, but it was one speed only and way too fast to be useful in the battle games I'm referring to