I have a 23" Cinema HD Display (the old perspex type with ADC plug - am currently using a Dr. Bott DVIator to get DVI signal into it from my MacBook Pro's DVI out) and I'd like to run my Nintendo Wii though it...

I've seen a few componant to VGA/DVI boxes and was wondering whether this kind of set-up would work with this monitor and the Wii?

NO. You need a scaler to get your Wii's signal to something that the Cinema Display HD can handle. There are solutions, like this (http://www.gefen.com/kvm/product.jsp?prod_id=4173) from Gefen. Other scalers are much more expensive, so this is really your only good option, and it was designed for just your problem--the demos at MacWorld had it hooked up to an Xbox, a DVD player and a Mac.