In game, it may take many more techs to reach civil service. But it is along a tech path that is a must have. Writing, Philosophy, on your way to Civil Service, Philosophy and Education. So in reality, Ironmen and Pikemen often show up at the same time.
It's often a question of when you stop on that path to education, and get Iron working. You could say that you can just beeline to Ironworking. And you can, but you will very often have some work to do after you discover Iron working, settling a city, then mining often being the best case scenario. If you're not out of luck and need to find it another way, buying when civ or CS eventually get it, then your strategy has been a waste and you will find the AI to be on even terms.
So very often by the time you get your iron men, the AI is fielding pikes. But when it does work, you go for iron and have it within your borders or get a quick hold of it, for a short while you have a clear upper hand.
Edit: looks like I posted in the wrong forum.