When the lamp turns on during each half cycle, its negative differential resistance characteristic will draw a large current spike through the capacitor.
Yes, this will shorten the life of the lamp and is why inductive ballasts were always used for gas discharge lamps such as fluorescent tubes.
At high frequency using a capacitor as a ballast works because the lamp never shuts off, but at 50 or 60 Hz the lamp, or at least a neon lamp, has to restart on every cycle.
The current draw of a neon indicator is so low, that a resistor doesn't need to have much of a power rating --capacitors will almost always be more bulky.
That said, I have used a capacitive dropper with an indicator lamp, but a LED,not a neon.
It wasn't off raw Mains, either, but a 65v AC control voltage from a transmitter.