Is it possible to use DC-restoration as a half-wave rectifier?
You capacitor value is too low to get good results with most diodes- the diode capacitance can be much larger than 10pF, especially with larger diodes. 

This circuit is similar to the voltage doubler used in many older microwave ovens. 

A mains-frequency transformer steps up the input voltage to a few thousand volts. A diode and capacitor gives you double the voltage for the negative half-cycles. 

Full description and animated gif from this website. Don't pay too much attention to the arrow or the direction of the arrow, it's the opposite of conventional current flow through the magnetron. 

 

Note that you do not get smooth DC out of this, you get pulses that are always positive (your circuit) or negative (the above circuit). That's fine for a microwave oven magnetron. It may not be fine for some other load. 

So, yes, it's possible and the above application has been proven practical in hundreds of millions of microwave ovens.