Yes, easy to imagine a chaotic situation causing distraction, or hyper focus on the wrong thing, etc.
What I have gathered from reading other forums about this, many pilots say they would interpret any significant undesired trim as a runaway condition, regardless of whether it was happening in intervals or it was literally continuous.
Others say that depending on training, and the policies of the operator, a much more literal reading of procedures is enforced.
I don't fly, but apparently trim is a very fundamental control for a pilot. It's easy to recognize when the aircraft is out of trim, and reacting to it is about as natural as it is for a driver of a car to use the steering wheel to keep the car centered in a lane.
So my assumption is, that with the AoA disagreement, and resulting multiple alerts and chaos in the cockpit, the pilots lost awareness of what the trim was doing.
I'm wondering if there's not a deeper problem within the air data systems. Why are the AoA sensors on new aircraft failing? They are just simple vanes, normally very reliable. The same ones are used on many different aircraft. So I don't think the actual sensor is a problem. But maybe there's something different downstream of the sensor itself. I would think if there were persistent problems with bad AoA data in 737s generally, it would have been addressed. Because the stick shakers, unreliable air speed, and everything else would still be happening regardless of MCAS.