[steely]

You can get the current measurement if you had a current probe.
An alternative would be to measure the voltage across a very small shunt resistor, and then converting V to I using the shunt R.
Were you looking for a waveform example of the current draw?
The scope would be better than the MM allowing you to see time with better resolution.
The draw should be constant of course, but using the FP mfr pattern as an example, you'd be able to see what yours in doing in comparison, but I am assuming that this was what you were after.