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. An obstruction is often added to the socket for this pin on the female connector, which means that the male connector cannot include pin 20; this ensures that the plug cannot be inserted the wrong way around.
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.