I'm close to 100% certain outlook.com won't work.
In terms of the screen real-estate issue, it's worth remembering that IE4/OE4 are from 1998. They barely fit in 640x480, because 512x342/384 and 640x480 weren't really the norm any more.
Newer PPC releases of most email client apps won't work either. Email just wasn't encrypted the way it is now until after all these programs stopped being developed. In addition, we're reaching the point where SSL root certificates in old browsers and network programs have expired, so even SSL resources that do or should work often throw errors.
We're even getting to the point where it's a toss-up as to whether mail.app in OS X 10.6 and older will work with any given mail provider.