What do you mean by "normally closed"? That usually is a term related to relay and switch contacts. If you mean - is the input to a mixer shorted to ground when nothing is plugged in, the answer is maybe but probably not, and it depends on the input connector type.
The switch must be connected with shielded microphone cable.
The switch should have gold plated contacts (it costs the same as high current silver contacts) because when the silver tarnishes then it will not short a mic signal.