I would try that but I stopped pc gaming a couple years ago and want to get back into it now and play total war again. Just wanted to make sure I could play on a HDTV before I start the build.
If you have a laptop, or any other PC that you can hook up to your HDTV, try it just to see how it feels. It can be another Total War game, or any game at all.
Keep in mind that most PC games are designed with very small text/fonts, and small, nuanced interfaces. They assume you are sitting at a desk in front of a computer monitor, and not on a living room couch with a TV across the room. If you're sitting more than a few feet in front of your TV, you may find yourself squinting pretty hard.
If you find yourself uncomfortable using your PC on the living room television, then you're certainly not going to be comfortable playing Total War. A 46" TV at 1080p should be fine as long as you're sitting close enough. A 32" TV at 720p I think is really pushing it, but try anyway.