With the 1N1007, but without the antiparallel diode, the LED will break down due to capacitive current during each cycle. However - the reverse current is dominated by the spike that occurs when the mains voltage goes through zero, and 1N4007 zero bias capacitance is about 20pF, so this will yield a current spike of only about 4uA for a few microseconds each cycle - not enough to damage the LED, I would think, unless there is some sort of degradation due to reverse current over and above power dissipation,which will be negligible.