Johnny T,
Sorry but not true.
Either zone control thermostat will control the shared pump independent of the other thermostats status. If yours requires both thermostats to call for heat, you have a problem that can be fixed or your manufacturer has done an incorrect install of your thermostats. Placing thermostats in series is not the way to do things.
I do agree that if the fan coil is blowing cool air and the circulating pump is not turning, then there is a electrical connection or the pump itself issue.
Trainer