If you get a TV card with the new PC that has either a composite or s-video input then yes, but it wouldn't be a very convenient setup to have in my opinion.
You wouldn't be able to watch TV without having your PC switched on and you wouldn't be able to use your PC for anything else while your watching TV
Actually thinking about it.... With a 22inch flat screen monitor there is a pretty good chance that it will have extra inputs so if your lulcky you may be able to connect the V box direct to the monitor.
But it still wouldn't be very convenient in my opinion to use your computer monitor as your main TV screen.