In a single diode rectifier circuit, is capacitor offering additional energy to Load?
Why can we get more harvested energy if adding the capacitor, even though the capacitor is not a source but an energy consumer (anyway, one of resistances).



You don't get more harvested energy - you get better managed energy.
The capacitor accepts power in short bursts during charging. 
The capacitor supplies power when the AC &lt; DC.
Most likely the circuit that you are powering requires steady DC rather than half-wave rectified power. The capacitor helps supply that.


Re-run your simulation with and without the capacitor and monitor the current at the top of Vin and the current through RL. You will see a big change in both.