I remember trying this when I was younger (with the Cheat menu). The primary issue is that while it is quicker, it is difficult to figure out the details of what is happening in the game when there is no pause at the beginning of your turn. Since the AI "personalities" of the different computer players cause some of them to be more aggressive than others, all of the games I tried to simulate in this way ended up with one military aggressive AI player dominating enough of the world that they did not need nuclear weapons.
There was a significant amount of variance among AI personalities and winning strategies in the various versions of Civilization I played, so I suspect that your success would vary depending on which version you were using. For example, if you were using CivNet, the multiplayer version of the original game, the anemic AI in that game might very well lock into some sort of peaceful stalemate, but the contentious resource model in Civilization III would probably produce different results.
There was a significant amount of variance among AI personalities and winning strategies in the various versions of Civilization I played, so I suspect that your success would vary depending on which version you were using. For example, if you were using CivNet, the multiplayer version of the original game, the anemic AI in that game might very well lock into some sort of peaceful stalemate, but the contentious resource model in Civilization III would probably produce different results.