[eluser]Pascal Kriete[/eluser]
There are two services coming together here. One is hosting, and the other is web development.
On the hosting side, you will have to see how your host handles these kinds of services. Subdomains can theoretically be done with just a wildcard dns and some mod-rewrite rules. All the other stuff, such as domain registration and email will require more integration with web-hosting services.
As for the programming. The short answer is: yes, CI can do this. However, be warned that this would be an enormous undertaking. I certainly wouldn't dare attempt this by myself. Ideally you would someone who is very skilled a writing solid object-oriented javascript, a good designer, and more than one experienced php programmer. By the way, it's neither jQuery nor ExtJS, but Prototype (and several thousand lines of custom javascript code).
Seeing as you are new to CodeIgniter - start small.
