It will with some, it won't with other. I have had mixed results. Is the switch has a button(s) to switch then usually it will work. Remember you do need a Lyra (or other PC keyboard interface) and a mouse interface between the switch and the Amiga.
Most switches "detect" if a machine is turned on by looking at the voltage on the PS/2 port, which means that if the switch is semi-intelligent it will not switch to the port unless a machine is powered on.
I use an Avocent 19" switch (16 port) which works like a charm.