Sure, it should work. Make sure that the ESC pixhawk and the receiver are powered from the same battery, to ensure a common ground. If you run the power cable to the ESC through a current and voltage reading sensor connected the the pixhawk, it should measure voltage and current.
If you connect the esc to the pixhawk and put the throttle channel to rc pass through, and than arm, (you would have to disable arming checks, prearm) you would get your throttle signal output and the current reading logged together.
i thought that this would be straightforward, but now trying to do it im not sure how to set all motor channels to passthrough. do you know how?
for no props (read no-load current), i think Stabilize mode will just work. if i add props stabilize would still work, but I would need to weigh the craft down or mount it.