If it is a 1:1 isolation transformer, AFAIK, all it does is remove reference to ground. Therefore I *believe* you'll have no problem, except you'll put extra load on it, which is not necessary.
Note: if you live in Europe, the PSU might have 220VAC input, while the monitor still expects 110VAC.
This is why in Europe we use 2:1 transformers only for the monitors and connect the PSU directly to mains, bypassing the transformer.