I do a lot of work using Immediacy (I used to work there) and I had thought about doing the same thing a couple of months ago. I think that the main issues would result from things like the plug-in handler, the idoc handler and (if your still using it) the ilink hander.
When you enable things like friendly URLS I think this would cause issues if you had similar named methods in your controller actions.
You may be able use some MVC in your project, I could see it working as an admin add-in but I couldn't see it being used to usefully in the main webroot.
I would think a CMS would have to be built using MVC in mind to get the most benefits from using the pattern, instead of trying to make it work in parallel with a pre-existing system API (limited as it is) and making more work for yourself.