Ground always plays a role. Ground is the return path for the current to flow from the battery, to the switch in start position, to the small lug on the solenoid, thru the coil, and into ground, which completes the ground path, since the battery (ground) is also connected to ground. Without ground (the return path), no electricity flows.
So, you will not see an open on the coil, unless the coil wire is broken. It should look more like a short (to it's housing/ground).
The key switch is only providing a current path for the small amount of current needed to energize the solenoid coil. When the coil is energized, it will push or pull the internal copper disc into contact with the other two terminals (one to the battery, one to the starter motor). Then the large amount of current needed to run the starter will pass thru the copper disc and terminals completing the path for the starter motor.