It's not as if Kirk was to be a "representative" anyway. He was just sent to escort Gorkon's ship.
The conspirators' intent of course was to get him to fire at the Klingons; some might have hoped to enlist Kirk to their cause, knowing him for a passionate and skilled Klingon hater, while others might have hoped to get rid of the inconvenient public figure.
One has to wonder about Spock's intent, though. It was he who took credit for the decision to send Kirk, both before the events and (in "Unification") after the outcome was clear. Did he really think in terms of "Nixon in China", that is, selling the peace overtures to the suspicious UFP public by using a hardliner as the messenger? Or did he feel the Klingons would be suitably impressed by Kirk and more likely to really start talking peace than if the UFP sent a soft-spoken diplomat? Spock must have realized that Kirk would have a very short time to have any sort of an influence over Gorkon, considering Kirk was just his escort and nothing more. So the second argument sounds a bit hollow... But Spock telling Kirk outright what the game was is also a bit dubious, as our Vulcan hero is a skilled liar and player at this point already.