I've used the capacitor method to provide most of the drop
in the past. I don't usually max out the LEDs at 20ma. I find
there is little difference between 10 and 20ma.
Yes, the 10 ( or 20ma ) is current flow through the capacitor.
It is necessary to have some resistor in series as well to suppress
line spikes.
You do have to be careful about mounting the LED packages, as they are
not rated for line voltage. That is, if you are expecting a UL rating.
Dwight