going from monitor to hdtv

I had a quick question. I just built a new computer and i am about to buy a new graphics card for it. I was planning on purchasing a 8800GTS 512. My birthday is also coming up and i wanted to buy a 42" hdtv for my 360. I also need a new gaming monitor for my computer because my 20" right now has a big crack through it. I was wondering if i could plug in my computer into my hdtv and just play my pc games on it. Also would this be better since the native resolution for the monitor is 720p which is less than the 1680*1050 that i currently play on. Cuz then it would put less strain on my hardware and i could always bump up the AA and AF since i am running at a lower resolution.

Games are fine but the desktop can be an issue. I always had trouble getting 1 to 1 pixel mapping on an HDTV, of course I usually use component, it might be better with HDMI.

I only ever do it for fun, I've got a 32" lcd hdtv right next to my desk, but my monitors are 26" and 24" so there isn't a lot of point in using the hdtv.

I played Oblivion on a 56" DLP at 720p, the lower resolution really helped keep the frame rate up. That tv had a dvi input which kept the image clear. I think it's too straining on the eyes to try and read a lot of computer sized text from normal tv distances (10') I found my eyes refocusing a lot more than with a monitor.