Storage of other speakers in the room, shorting them while not in use? Myth or true?

This might reduce the tendency of the cones of the unused speaker to vibrate from the sound put out by the active speakers.  You are not "shorting" the speaker, but, rather, completing the circuit.  When the circuit is complete, the movement of the voice coil in the magnetic field of the permanent magnet induces a current (but only if the circuit is complete), and that current, in turn creates its own magnetic field in opposition to the field of the permanent magnet.  In effect, this stiffens the cone's resistance to being moved by the vibrations in the room.  How much this actually matters to the sound in the room is debatable, but, there would be no harm in doing this

Here is the experiment--take an unconnected speaker and push on the woofer cone to feel how much resistance to movement there is.  Now, connect a wire between the positive and negative terminal and push on the cone.  You will feel resistance increase (the now completed circuit will create a magnetic field  that resists movement).  I have my doubts that this will make any real difference in the sound in the room, but, this at least explains the theoretical basis for the practice.