Check the manual of the switch if it simulates a connected monitor for the client.
Some clients are picky when it comes to unplugging monitors or booting without one.
Wayland also seems to do something weird when the monitor is off (I have some applications where the window becomes tiny when turning off the screen).
Exactly. Your KVM switch need to support it, or your clients will always act like you unplugged the screen when you switch between them.