Do regulations permit an airliner be equipped with a radio transmitter which cannot be controlled by the crew? In response to the case of MH370, an idea which has been floated is that of a device to transmit an aircraft's GPS position. Not specified is whether such a device would be operable by the flight crew.

Among the scenarios suggested to account for the aircraft "going dark" and its apparent flight path is intentional action by someone aboard.

To provide aircraft position (or any other parameter) reporting free of any possible interference by anyone aboard the aircraft would require installation of equipment inoperable by and therefore in a location inaccessible to anyone (crew included) during flight. That means such equipment could never be powered down while the aircraft is in flight.

Have there been/are there currently any regulations which would prohibit the installation of such a device for any reason - e.g. fire safety, possible interference with other radio equipment essential to safe flight (navigation, communication)?
All equipment on board needs to be interruptable, either by direct control input (turning it off) or via circuit breaker. This especially holds true for equipment that is capable of broadcasting or emitting radio waves, such as radio telephony equipment or the transponder. 

If the transponder for any reason became damaged and started to send incorrect replies to ground interrogation, it needs to be shut off in order to not confuse ATC systems or other aircraft's TCAS. Electronic or electric systems also need to be shut down in case of eletrical fires or other safety hazards to the aircraft.