Dell offers (as far as I know) 3 All-in-one desktops: Inspiron 23, Inspiron 24 and XPS 27.
Did I miss any ?
I can't find a thing about people running Linux on it.
I wan't to run either Arch or Debian on it.
Has it been tested, is there a reason it wouldn't work? It's quite expensive and I won't use a Windows system if the Linux thingie doesn't work out.
I can't think of any reason it wouldn't work, but it's definitely not guaranteed. Linux does not excel on the very latest hardware - it is behind schedule supporting the latest hardware, so don't go nuts.
Ubuntu 12.04 is officialy suppoted on the Inspiron 24 5459. Try it and let us know how it goes.