Sure capacitors limit current. They have impedance.
Xc=1/(2*pi*F*C).
Having said that, you still need to be sure you don't exceed the reverse voltage limits of the LED, and the current will not be DC, it will be "pulsating". A big problem is that line transients can create big current spikes which can damage an LED. Nevertheless, LEDs have been driven successfully off the AC line using a capacitor (and maybe a series resistor and/or inductor) as a current limiter.