I don't know 139 either, but fair chance it has AHRS and solid state laser gyros and they only take a few moments to come on-line. And before doing any instrument departure you always do an instrument check to confirm proper operation. I doubt very much attitude reference instrumentation has anything to do with this. There was an eye witness at the departure point who saw the aircraft lights disappear into the sea, associated with a loud bang, moments after takeoff. They didn't get very far at all. Short of the tail rotor having fallen off, or some uncommanded hydraulic servo event, it has the hallmarks of a CFIT event. If all the passengers were still strapped into their seats, as reported by the divers, then the entry into the water was probably violent and incapacitating. Supported by the rotors and top deck cowls all missing from the underwater vision. They've probably gone in sideways or upside down.