I'm amazed at the amount of "needless" speculation for a relatively simple event. The PF simply failed to respond correctly to what should have been a non event. Had he followed his training and flown pitch and power then this is just one of dozens of similar incidents that plagued the 330/340 series.
His error was compounded by the senior pilots (on flight deck) failure to exercise command authority even though he knew the PF was over-matched by the situation.
I do not believe the aircraft was recoverable by the time the Captain returned to the flight deck however I do believe his failure to assume command (as PF) was an incorrect decision.
There is no indication that the initial climb was anything other then a response to stick inputs by the PF. Further the trim was a response to his continued application of control input. There was no autopilot or system induced "runaway trim". The aircraft was perfectly flyable from the moment AP disconnected until it hit the water.
At the end of the day the lesson is simple...the more you en devour to remove the aviator from aviation the more likely you are to have this type of end result.