It's quite likely that many LEDs will flicker. The exception would be those that are powered by a DC supply rather like a laptop PSU. Many of the standalone drivers are "constant current" devices that use PWM to regulate the current. Most external car lights (including some headlights) are LED and you get a fairly obvious strobing effect from them.
Mains bulbs don't have the space or the need to accommodate the components required to provide a flicker-free output. I noticed that the trendy "LED filament" bulbs are little more than a series capacitor (to limit current) and a bridge rectifier. They will certainly flicker at 100Hz.
If you do the sums, you will find that a capacitor that will store enough energy at around the typical bulb voltage will end up about the same size as the bulb itself – and cost more. The PSUs mentioned in the first paragraph store their energy at ~340Vdc and the required cap size is significantly smaller.
I'm not convinced there is any significant risk unless you are stone deaf, mind.
Murray