That would be impossible, unless some part of the campaign was actually unbeatable. If it is beatable, then a method to beating it definitely exists; even if it changes by AI (unlikely), a method would still eventually be picked out at random.
Oh, if it is impossible maybe you should prove it, then. Use a random calculator to determine the size and composition of your force, then defeat at least one opponent at multiplayer (including vs. AI) StarCraft (excluding anything under "Hard" as that hamstrings the AI). I'll then post evidence of a player fighting a boss over and over again using dodge and attacking until he wins, even better, I can show PvP battles where the players only use dodge and attack.
Basic Chaos Theory will show that you'll never win a game of StarCraft unless your opponent is also choosing a random strategy, something AI or a player would never do.
I would say you could just use a video, but funny enough, there is no one who plays StarCraft by using a random trial and error strategy, there hundreds of videos of players using trial and error to beat Dark Souls, though.