Connecting Consoles To Pc Monitor

[Steve-O]

Im thinking of getting a LCD Monitor that has a DVI and VGA Port. Am I right in thinking that If I get a VGA Box that I can have the LCD Monitor connected to my PC Via DVI and connect the VGA Box to the monitors VGA Port so when I want to play my PS2 / Xbox etc all I need to do is have the LCD Monitor on and leave the PC Off??

Thanks