Well, yes it's possible, but not a great solution. You'd need a computer to drive it and sadly the mac mini can't do that (it can only drive the 23"). And a Mac Pro might be a little bit of overkill for a home entertainment system! Obviously you could use any PC that has a capable graphics card. Then you could add a digital tuner (elgato's are OK) for your freeview and programme guide, and hard disk recording. And of course your computer would also be able to function as your DVD player.
The real problem, though, is that the resolution of the 30" display is so high. That's great for computer work, but not so great for watching TV - because there's a huge gap between its native resolution and that of the content you'll be watching. Even 1080p content is likely to look a little blocky, and standard def content will likely look terrible.
Short answer: yes, but I wouldn't recommend it!