You'd be better off dimming by using an array of current-limiting capacitors and SSRs (a power DAC, as it were).
Common mode chokes saturate above some mA, beyond which their inductance quickly drops to a tiny fraction of the zero-bias rating. There are also ground-return chokes, made the same way (a single winding on a high-mu core); they are intended to saturate under fault conditions, providing a low impedance ground path, while under normal conditions choking high frequency currents (which can be sometimes beneficial, hence their existence).
You need to shop from inductors -- specifically, one rated for saturation current higher than the peak current seen in circuit.
You also need a proportionally larger inductor at lower dimmer settings. Size it for the lowest current you wish to maintain continuous light output on.
An inductor can indeed serve as the energy storage component, but very large inductances, rated for reasonable currents (e.g., 1H and 100mA), are neither cheap nor compact. (They are at least available, amazingly enough -- Hammond Mfg. for example.)
Incandescent lamps do modulate some, though you usually need an instrument to do so -- the hum is clearly audible with a photodiode for example; it's hard to observe this by eye. Other traditional sources, like fluorescent lamps and discharge tubes (sodium, mercury vapor, halide) are easier to see, tending to leave a "string of beads"-like track in your visual field when you move your eyes quickly past them.
LEDs respond quite quickly, the blue source having a useful bandwidth in the 10s of MHz if driven properly, and the yellow phosphor having a decay rate in the 100s of ns. Next time you're walking past a string of LED xmas lights, see if they flicker as you move your eyes around.
Tim