Not quite. The current is decided by the combined reactance (XC) of the capacitor and the resistors added together. If you increase the capacitor value you decrease XC and the current increases. Similarly, if you increase R the current decreases. The opposite happens if you change the values the other way. You share the voltage drop between XC and R so by just dropping R you have increased the LED current. You could remove R altogther if you had the exact value of C and you could remove C if you had the exact value of R. the reason C is used is it has almost no power loss while R has a large power loss.
For example, if you removed C and relied purely on R, the value would be 2.4K but it would dissipate almost 12W of heat, over three times more power than the LEDs consume!
Brian.