The refresh on lcd is 60hz which is identical to hdtv specs, so a crt with a higher refresh won't affect the overall quality of the picture. PS2, Xbox, Gamecube, they all run at 60hz, regardless of what they're plugged into.
You could also run it through a tv tuner card... however, I'd recommend against getting an add-on card, and go for a video card with a tv tuner built onto it. I've gone through 3 different add on cards in the past 3 weeks trying to find one that will allow me to hook my consoles up and play some games, the best one (ATI TV Wonder Pro) had about a half second delay if
"Best Picture Quality" wasn't checked... and of course it looked like shit. If "Best Picture Quality" was checked, the delay increased to 1 second. The worst card was a Diamond XtremeTV PVR550, running without de-interlacing, it had a 2 second delay... almost 4 seconds with de-interlacing. And the software for the Diamond sucked ass. Avoid SnapStream's Beyond TV... it's quite possibly the worst piece of software I've ever dealt with.
My monitor has svideo and composite video inputs, in addition to the standard dvi and vga connections. But I want to be able to take screenshots while I play, or record replays without having to waste memory card space. Neither of which can be done with the vga converters, or plugging directly into the provided ports on my monitor.
I just took back the last of the add on tv tuners, and placed an order at newegg for an All In Wonder 9600XT. It's only about $70 more than the add-on tv tuners I was trying, and I know the AIW 7500 I have in my htpc had no problems with being able to play games through it. I can only imagine the AIW 9600XT will do the same. I would've just used the 7500, but I need something with a little more oomph for pc games