Resistor may or may not be needed. Think about what happens when you first plug it in. If the line voltage is just nearing peak, you will have a huge surge of current. Based on your thread title, you probably already know this. I the rating of the LED is high enough, you don't need the resistor. Otherwise you do. First you'd need to construct the current waveform, but without knowing the impedance pretty well, you could only take a WAG.
Unless one component has a resistance that dominates, i.e. a resistor, you need to know the impedance of the line, power cord, switch, rectifiers, capacitor, LED, and anything else in the circuit. Those are all normally quite low and poorly characterized, particularly under extreme (high current) conditions. My crystal ball is pretty cloudy lately. How's yours?
Of course, peak non-repetitive pulse current is not a spec that's usually published for LEDs, so you're left to speculate, and have a 'spirited debate'. Cree has a document about pulse applications. It might prove insightful, but I haven't read it.
If you haven't already considered it, the worst case is when you are connecting the device to the line, and have a half-cycle 'bounce' or brief disconnect. That way you can have the cap fully charged one polarity, and suddenly apply full voltage of the opposite polarity. That way you can have twice the peak-peak line voltage driving current in your circuit.
I don't know where you live, but even 200V in a low-impedance circuit gives a pretty massive current spike. Some places it could be 480V! I'd worry about exploding the bond wires.
