Arcade monitors are just like TVs, the reason you get the somewhat distorted picture is because the game makers decided to make a cheaper PCB that uses less memory and CPU power to output the full screen resolution. Instead of using the full scan lines they use every other one. So game consoles will look exactly the same on an arcade monitor since its the game console putting out the signal. The only thing that makes an arcade monitor different than a TV is the Tuner components an added RF signal componants. (and speakers)
The only problem with connecting a home console to the arcade monitor is the adapters needed, which some are crappy and make the picture suck. Vice versa for the TV inside an arcade game, you need an adapter that coverts raw RGB S to S-VIdeo/Component or whatever it has and if the adapter is cheap then the picture will suck.