I've done it. I save the game right before I'm about to uncover a barbarian hut, then move onto it. If I don't like what the random number generator gives me, I load the saved game and do it again. Over and over again.
See? I've played ONE turn of Civilization, just repeated about 50 times.
Early game, no. Late game, it can take 5 or 10 minutes per turn and you may be capturing more than one city per turn during an invasion, I can see it working.