Supercap overvoltage protection
The circuit does not appear to work.
Consider the situation where the Supercap is at zero volts, and the inbound coupled signal results in U1 supply increasing by charging C2. So far so good.
 ...the FET is initially off and will begin to turn on only once the supply rail exceeds VGS(th)(though IMO you need a pulldown resistor to ensure this turn on). The turn on level is about 0.6V, far below the operating point of the op-amp. In addition, the op-amp has both inputs at zero volts, though admittedly you only need mV of input signal to start to get a response on the output (once you have sufficient supply).  

With both the inputs to the op-amp at zero volts, the op-amp can only provide enough signal to get the FET to conduct (uA - mA) with the output stages biased, the FET will then start to discharge the voltage on C2. Unfortunately the output of the op-amp LT1803 is not in working range below 2V, so what output you get is unknown, and the current through the FET likely only uA.