If the room already has isolated power, then I believe the monitor would have to be on isolated power unless it is fixed, listed theraputic or diagnosic equipment.
See 517.63(B), which I would believe applies.
Generally, when you put a procedure room on isolated power, you put everything on the isolated power with a few exceptions. The exceptions are for recessed lights which are out of reach, and specalized equipment like Xray equipment that may be difficult to supply from an isolated system due to its higher voltage or current requirments.