Allo Partholon
So far as wireless K'Board/Mouse etc. are concerned, I'd guess the distance from the PC box to desk would be approx 4 feet or less so, unless you have steel beams passing trough the wall, there shouldn't be any problems with that - My logitech K'board/Mouse has a range of at least 20 feet through several concrete walls (I can't test it any further, I run out of apartment
Re: USB CD/DVD burners, the main 'snag' is that USB-2 is only 480Mb/second, so you'd be burning/reading CD/DVD's veeerrry slowly. I know that external drives are available, but to date, that's their biggest drawback, slow speeds compared to internal units.
Unless you can find an extension monitor cable, you'd be limited to positioning the system by the length of your present cable on the monitor.
Depending on the size and specs of your rig + the length of time that it's on, you might need an air-vent in the closet, just to let some cool air in, otherwise you'd be recirculating the hot air from the PC, warming it up each time through the box.
[Thinks] With some cunning planning, you might be able to use an 'extractor' fan to pull the warm air out of the closet and use it to help warm the main room up
It's an intriguing idea though, as you say, you shouldn't have any problems with noise etc.