To follow-up my previous measurements on the current draw of the LDD dimming circuit I enlisted the assistance from someone who knows more about electronics then me. It turns out my measurements were sort of correct, I just had a decimal point in the wrong place.
So, the actual measurements are:
100% duty cycle - 7.7uA
0% duty cycle - 53uA
Please note that these are micro amps rather than milli amps. So, in effect, we are never going to get close to exceeding the current limitations of the Arduino pins or board.