Humans don't perceive a blink rate above ≈40 Hz so it won't appear to blink at 60 Hz.
This may be the schematic you want: AC-LED. Whenever you apply AC to an LED you need to protect it from reverse voltage with a diode in reverse parallel as shown.
If you used a 1Mohm resistor to limit the current, then you are going to create serious inefficiencies in the circuit. You will be dissipating a lot of wasted power through that resistor (I^2*R).
An 100 or 120nF X2 rated cap with a series 1000 ohm surge limiting resistor (2W, 500V rated) will limit the current to near 10mA, put the LED in a bridge rectifier, (any 4 diodes with a V>5V and I>50mA will suffice) and this will work fine, for a triac dimmer input, worst case dissipation on the 1000 ohm will be 0.8 watt.
(for 5mA rms in the LED use 68nF X2 and so on...)