Is it safe to power a monitor without grounding?
If grounding (PE) contact is in there, then it must be preserved, unless you really know what you are doing. Having things grounded properly, if they are designed to be, is very important if you would try connecting or disconnecting two devices. Both grounded properly through the receptacle -> no potential between cables' grounds or shields when they are in disconnected state. Leaving PE disconnected may (will) create virtual ground (depending on the internal circuit of the device) which may be up to half of mains AC voltage potentially shocking the person connecting or disconnecting the devices, and potentially damaging inputs/outputs of the devices.