GNU screen only needs a terminal emulator to work. I've used it with lots of different ones, and pure console as well. I'm using it now with urxvt and ratpoison.
if scite is extensible enough, scite should call ipython and show the prompt in a buffer (or however you call that in scite slang).
Actually that kind of things are what vim cannot do (and its author won't implement because vim is *JUST* an editor), because it requires asynchronous socket handling to comunicate with ipython.
Emacs can do it, and in fact, a quick google search showed that an ipython mode already exists

It would be KILLER to have IPython + SciTE under Screens on Xmonad. Is this a crazy idea?
well, there are some incongruences there:
scite under screen: screen is for terminal apps and Scite is a X app. you can't embeed scite into a terminal.
ipython+scite : probably. if not, try emacs. or vim+screen.
Look the different approaches: emacs tries to get all the functionallity inside itself, so the user is always 'living' in the emacs world, getting lots of synergy benefits. vim's approach is 'do one thing and do it well'. a typical vim user would use screen with vim and ipython inside. No idea for the scite+ipython combination but google didn't show any relevant results at first glance. You probably can't extend scite to theese levels...
no problem using them under xmonad nor any other tiling wm.