You should look at the location of the water valve, (solenoid). If it is at the bottom of the refrigerator, the water is pushed up the line by pressure each time water is called for to fill the ice maker. This means, letting it run a cycle with the water off will not clear the line of water.
I might suggest to open the line above the solenoid and allow it to drain. Of course, you will need some air in the line so that it will drain. Also, there will still be water in the solenoid. You do not have to worry about the part of the ice make contained within the freezer as it is normally kept below freezing by design.
One could open the solenoid by applying current to it, which would allow it to drain if you have removed the supply line.
The concern would be the supply line, the solenoid and the line going from the solenoid into the freezer/ice maker.
I am sure someone has done this before and knows the proper procedure.