Most likely. Even with a cracked gear, the arm will still move.
There are some pictures in the article that will shed a little light on things. The air mix actuator is basically a small motor assembly that moves the air mix door allowing more or less heat to pass into the cabin. Simply put, the door is connected to a rod which is connected to the white arm. The arm (part of the actuator assembly) is connected to a shaft which is connected to a servo motor via an array of gears. The motor is directed to open or close the air mix door by the HVAC controller.
There is a large gear inside the actuator that is pressed to the shaft (that'* connected to the white arm). This gear has a habit of cracking or splitting. This reduces its "hold" on the shaft which allows the gear to slip on the shaft. When this happens, the programmer loses track of the position of the air mix door and starts flashing the ECC display because it wants to be calibrated.
For some reason, disconnecting the battery seems to be a player in making problem manifest itself. When mine started going bad, before I had a clue what was happening, I just ignored the flashing ECC and eventually it corrected itself. As the crack in the gear worsened, it got to the point that the gear slipped on the shaft enough that I could see a jerky motion as the white arm moved from hot to cold, and the white arm wouldn't move it'* full range consistently. When I finally changed my actuator, my gear was cracked over 75% through.
You may be able to force your actuator into compliance for a while, but I suspect you will eventually need to replace it. Although... I have been known to be wrong more often than I'm right.