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The reason Clyde doesn't count toward the 120 is that he unfriends you after the tutorial, so you have to talk to him prior to talking to Cartman for the first time. Even though he unfriends and you and isn't in the final count, I do believe he counts towards the trophy.
Even if it's found that he doesn't, it's better to be safe than sorry and talk to him first thing anyway. Otherwise, you missed out on a lengthy trophy in the first couple minutes of the game.