Could a rear center of gravity position cause an airliner to lose control when a pitch-up is commanded?
On virtually any swept-wing design, "wingtip stalls" are a danger. Most light aircraft are designed with a straight wing and a leading-edge contour such that the inside of the wing stalls first. This has two advantages for light craft; first, aileron control is available as long as possible into stall entry, allowing roll control and thus the ability to stay coordinated. Second, the departure of airflow over the top inside of the wing will reduce or eliminate the downwash of air over the horizontal stabilizer, which normally corrects for a slight nose-heavy CG. With the balancing force gone, the normal response of the aircraft will be to nose down, restoring a lower AOA and building forward airspeed to let the pilot recover quickly.

With a swept wing as is seen on modern jet airliners, the wingtips tend to stall first instead, because the airflow over the swept wing lowers the stagnation point and thus the effective angle of attack of rearward sections of the wing, so the wingtips at the rear will exceed the critical AOA first. 

When the wingtip stalls first on a swept wing, two things happen. First, aileron control is severely affected, making it harder to stay wings-level and avoid entering a slip or even a spin. Second, the center of lift from the unstalled portion of the wing moves forward, placing the CG further behind it. An aft CG works against pilot efforts to nose the aircraft back down to recover, and in an uncoordinated stall the aft CG will keep the tail of the airplane "outwards" from the center of the spin, hindering or preventing efforts to cancel out the rotation with the rudder as the vertical stabilizer will be stalled due to the extreme "sideslip".

This is a potential problem in any airliner, where the weight is distributed along the majority of the fuselage. Any significant deviation from mean values for per-passenger or per-bag weights can place the CG too far aft. Tail trim tanks can further exacerbate this.

However, Air France 447's crash, in my amateur analysis, was not caused by trim characteristics. It was primarily caused by the pitot tube icing. This had several detrimental effects on the flight crew's situational awareness:


The disagreement of the plane's two pitot-static systems cause the flight director to unexpectedly disengage the autopilot, setting the flight crew on their heels.
This same disagreement in the pitot-static data also caused the flight director to switch from "normal law" to "alternate law 2" which among other things disabled roll and pitch/AOA limiters, as the data used to calculate those limits is no longer reliable.
Lastly, the lack of reliable pitot-static data was reflected in cockpit instrument displays. We don't know exactly what they saw because information on the status of the right side pitot system is unavailable (it was not recorded by the black boxes). However, we do know the disagreement of data caused the red-flagging of practically all information reliant on such data, including the airspeed and altimeter tapes, the flight director, velocity vector, and all secondary indicators including AOA readouts, the stall horn, etc. The flight crew would have been totally reliant on external visible references to determine the aircraft was stalled.


A secondary instrumental cause was the stall indicator system itself. Counter-intuitively, the stall warning was issued when the aircraft was nosed down, and stopped when the aircraft nosed up. This was due to the flight computer treating the extreme AOA calculations (in excess of 40 degrees) as unreliable. Nosing down brought the AOA back into the "reliable" band, but the resulting alarms were counter-intuitive to the pilots; applying a control input and hearing an audible warning is usually a signal to back off that control input.

Finally, the flight crew themselves demonstrated a lack of familiarity with the behavior of the aircraft in exceptional circumstances; the loss of pitch/roll limiters and the counter-intuitive stall horn behavior caused the flight crew, in the absence of the captain, to make a series of critical and ultimately fatal overcorrections and inactions.