If there are any doubts if the pilots would be aware that the aircraft is automatically setting the trim nose up - please have a look at this video. Those wheels are painted alternating black and white for a reason.
Ask most Airbus pilots if they actively see the trim wheel moving and the answer will most likely be "No". It moves silently - unlike the Boeing system - and it is so effective in normal operations that it's not actively monitored. In an airplane that is supposedly out of control for "unknown" reasons, it may not be intuitive to look at something you don't normally see.