This is an interesting question. From a pure research perspective, you would impose a minimum threshold in the incident power and consider your harvesting successful if and only if this threshold is met or is exceeded. From a practical perspective, it depends on the transmission frequency, the wireless channel, and then circuit sensitivity. Powercast, a wireless power transceiver, has a sensitivity of about -22dBm. 

Hope this helps.

Current state-of-art is approximately 200us*10uW=2nJ (order-of^magnitude approximation)

Most of time to start wireless circuit is spent on high-Q oscillators (quartz) frequency stabilization.