Every flight controller (with the occasional exception of the FIDO officer) was expected to listen to the air-to-ground loop any time that the crew started transmitting, so that the crew wouldn't have to waste time repeating themselves and also to ensure any urgent questions or comments were addressed. Any controller who repeatedly failed to do so would usually find themselves shown out of the MOCR with another controller to take their place.
But even on Apollo 13, some controllers would be caught flat-footed. Below is a list of links to instances in which FLIGHT reprimanded the controller for apparently failing to listen to the loop.
Link 1:
060:47:52 - Black FLIGHT (Lunney) to INCO (Scott)Link 2:
073:24:16 - Gold FLIGHT (Griffin) to CONTROL (Wegener)Link 3:
084:28:16 - Maroon FLIGHT (Windler) to FAO (Gardner)And at about 139:39:11, a little bonus clip here where YAW (I think Pressley or Wells?) tells INCO (Hanchett) to listen to the air-to-ground
during an exchange that essentially amounts to YAW saying "We're too busy to do your work, INCO."