The really cheap ones may be mechanical switches. Most however are digital switches.
Digital switches respond to requests by the PC for PS2/USB/Monitor even if it's not switched to the keyboard/mouse/monitor, whereas a mechanical switch must be switched to the PC to talk directly to the keyboard/mouse/monitor.
In rare occasions, switching with mechanical switches can hang PC's. I'm not really sure why, although I can hazard a few guesses.
In all occasions, restarting a PC without the mechanical switch turned to the restarting PC will cause the PC to not initiliase the PS2 circuitry, or recognise the vid port as the primary monitor.
Some video cards will therefore not initliase the video port at all. Mostly older vid cards (gerforce 4's or earlier) I've experience this with. The PC will fail to recognise any PS2 devices plugged into the PS2 ports (or switched to the ports) if it has not initiliased the PS2 circuits.