Yes, you still have have the conditioning step. What I normally do is keep my beers in the fermenter until they are ready, and then keg them and stick them in the kegerator and carbonate them.
You're correct that carbonated green beer is NOT ready to drink- it's just not flat any more. Many of us keg after a couple of weeks in the primary, then do the "secondary" or conditioning phase right in the keg at room temperature. Beer takes a long time to condition at cold temperatures, so if it's young, it's probably more practical to condition it at room temperature and then stick it in the fridge.
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