With no explanation, label text_A→text_B with either "DON'T KNOW", "NO" or "YES".
text_A: In the ATA standard, pin 20 is defined as a mechanical key and is not used. This pin's socket on the female connector is often obstructed, requiring pin 20 to be omitted from the male cable or drive connector; it is thus impossible to plug it in the wrong way round.
text_B: Does it sound like the order of the other pins is necessary for proper functioning of this connector (as in, they would not work if the pins on the top right row were inserted into sockets on the bottom left)?
YES.