Let's assume that to drive the MOSFET, we need to provide a current of 100mA and for the UC3842 20mA. So, for example's sake, we need 120mA current. It'll take some time to charge the capacitor, but it's going to discharge very quickly. Each cycle, you need to drive the MOSFET, but the capacitor is probably not going to charge that quickly. So, the UC3842 might turn off, or even if it doesn't, the MOSFET may turn off. So, the output will be 0. So, the output will be 0 for some time, then you'll get output for a short time during which capacitor is charged, and then again 0.
And say, you had managed to make the capacitor charge quick enough. So, if we had an average current of 120mA, we would have a large loss. With 325VDC input and assuming the zener is rated at 30V, the loss in the dropping resistor would be 35.4W. Also, the condition for zener regulation is that the current should be less than 30mA, which as we can see, it clearly isn't. So, you risk burning the IC as well.
And so, you should use an auxiliary power supply.
Hope this helps.
Tahmid.