Don't anyone take this the wrong way, but if you have to ask, you should

Running a monitor with an isolation transformer that doesn't require one won't hurt anything.
Running one that does require it without one, will hurt the monitor, the game board, your fuses or yourself.
But to specifically answer your question, yes, the Nintendo monitors require an isolation transformer... **** BUT **** not just any old isolation transformer, they require a STEP-DOWN isolation tranformer.
They're built in Japan for japanese voltages which are 100 volts and not 110-120 like they are in the US. If you connect it without reducing the voltage to 100 volts, you will blow it up (a few key components will fry on the monitor chassis).
You will need a 1.1 : 1 step down AC isolation transformer in order to run a Nintendo monitor. Get one out of an old Nintendo cabinet.