now days nearly every product has a smps power supply for its working for eg, computer, tv, mobile phone charger, dvd players...every thing now days have a switch mode power supply....and in this there is certain amount of filter involved in them to make them work properly so I dont think it is a problem to connect the monitor direct to mains until there is some major fuctuation in the line as the power from the mains is quite clean from spikes or anything like that.....
to check for a fuctuation take a DMM and check the voltage variation