Not quite.The autopilot trim system also runs at two speeds ( high or low) depending on the flap position.
Well sort of. The high speed AP trim though is equal to the manuel electric trim speed with flaps up. The AP flaps up trim speed slower still.
From Boeing:
Normal electric trimming of the stabilizer is done at one of two rates as controlled by flap position. Trim
rate with flaps retracted is 1/3 the trim rate with flaps extended. The autopilot actuator also trims at
one of two rates as controlled by flap position. High speed autopilot rate is equal to the normal electric
low speed rate. The low speed autopilot rate is 1/2 the rate of the high speed autopilot rate.
So in manuel flight with flaps out , the trim wheel moves three times faster than depicted in the video.