Just adc the voltage on that 330ohm resistor - it gives you the current.
Now, that is highly simplistic: it assumes that if you sense a current on that resistor, there is current going through it (to ground). It is entirely possible that there is an open circuit so there is voltage on the resistor but no current going through it. You can software detect that.
to "sense" when the LED is illuminated.
That is actually quite different from sensing the current: you can have current going through an LED yet it is not illuminating.
If you really want to sense illumination, use a light sensor (photoresistor / diode / transistor for example).