As it was mentioned in some materials linked above at the topic, the game stores the data about the keys (buttons) pressed by the players at the following locations:
Player 1 keys (tapped): $008E
Player 1 keys (holding): $0091
Player 2 keys (tapped): $008F
Player 2 keys (holding): $0092
Each variable is a collection of 8 binary flags, each representing a key on the controller. This data is used by the game to determine what a character should attempt to do next.
When the CPU Player is participating in the fight, he uses the same addresses to issue commands to his character. In other words, he "presses" the keys as he would do as a real being. At least theoretically.
When the CPU Player presses a key, the variable with flags seems to be rewritten for the rest of the frame, so it is practically impossible to hi-jack the control from him. At least right now. Yet, there can be moments when the human can make his keys heard, but only when the CPU Player is not pressing anything, which in most cases happens when the character can't move anyway (e.g. during a pause) or it doesn't know what to do (at the bonus game). Right now it is unknown would the game even care to handle such input while the CPU Player fights (or at least bothers to do that).
If the game is paused the CPU player seems to stop pressing any buttons yet when the fight continues he resumes his actions immediately, so hitting PAUSE button would not force him to stop running or doing other actions requiring to hold a button (pause also freezes special charge timers).
Since the CPU Player obviously doesn't use a controller, his input does not appear in the input registers and emulator can't display it by itself.
So I wrote a simplistic LUA script that displays the input actually registered by the game, including that from the AI. Running it might show how the CPU player actually handles the character and when the input from the human player gets through.
http://pastebin.com/RvuszZcx
P.S.: right now the script doesn't really differentiate tapping keys and holding them (since the holding flags are arisen at the same time as the tapping ones and descent when the keys are released), yet I might implement that later.
