No, you don't. "On rail" parts which go too deep into the atmosphere just disappear. This even happens when they would have survived the landing (for example because they have parachutes attached). To recover a part you must supervise its landing. This means that it is currently hard to recover the first stage of a rocket, because you can not supervise both the upper stage on its way into orbit and the lower stage on its way back to ground. So no Grasshopper launch system yet.
However, I did construct a launch system which has a first stage of solid rocket boosters (which are dirt cheap) and a reusable second stage which can bring a payload of up to 15 tons onto a sub-orbital trajectory. After leaving the atmosphere I can detach the payload, use the payloads engine to get it into a parking orbit, and still have enough time to switch back to the second stage before it despawns so I can land and recover it.
Here is a screenshot of the system with a 15 ton payload on top.
Also, you can only recover a part which has a command pod attached to it. So if you want to recover a stage, you need to add at least a probe core to it.