Yes, things take time to happen. For example, in MMORTS, it can take many hours just to construct a barracks. But luckily, if you start a barracks, train some archers, and send some peasants to go farming before logging off, 12 hours later when you login you may find your barracks completed, your new archers awaiting orders, and your food stockpile increased quite a bit.
Though keep in mind, the longer you are away from your city the slower the automatic gathering gets. I guess your peasants get lazy when they realize you aren't watching.