Hard to say as it depends upon the quality of your supply. I the load on some of the voltage rails suddenly drops to zero (by disconnecting a game board), the voltage could jump up a little for a fraction of a second. If you connect another gameboard, it might get a higher voltage than it expects. So basically, the correct procedure guranteed to work without issues would be switch supply off, wait a couple of seconds, switch gameboards with a relais or mosfet or something similar and turn on the supply again. A good power supply should be able to soft start under load and reach it's expected output voltage pretty fast without overshoot.
