Game consoles through a TV tuner

Hello, I do not own a TV and I was wondering if I bought a cheap TV tuner I could play my GameCube and my Ps2 through it, or if it would have poor picture quality or lag. A Google search turned me up with people saying it works great on cheap cards and others saying it just doesn't, and I wanted some clarification on this. I have seen those converter boxes that output VGA, but I have my Xbox 360 connected to my monitor's VGA port and I don't want to be hassled by switching out the VGA cable all the time.