Not necessarily, there are two separate valves. One for the water through the door, the other to the ice maker. One solenoid or valve can stop working and the other can still work fine.
The tube that carries water through the back of the freezer compartment can also freeze solid and not allow water to get into the ice maker. The tube steps up to a larger size inside the freezer cabinet and it is angled downward so it empties after filling to avoid freezing, but it still can happen.