I think this is a good idea. I don't have to explain what the advantages would be; the question covers that enough, I think. There are two things I'd like to do with the answer: giving an optional design and discussing the developer's pain to create this.
It could look like this (I used the Electrical Engineering site for these images):
As you can see, I added some options directly above the preview: inline, side-by-side and side-by-side markdown. This is exactly the same as when you're viewing revisions. Because I added a normal option, you won't lose any features you have now!
Now, let's see how it looks when viewing it with, for example, the side-by-side view:
I assume the revision change views are done with the pecl Text-Diff package or its newer version. That means the changes are calculated at the server. That means, there are three options (I think):
Continuously use Ajax calls to the server, like every 10 or 15 seconds. I wouldn't recommend it, it would increase the server load a lot, probably.
Use an Ajax call, but on demand. So only call the server when someone actually clicks on a side-by-side button. I (and the OP) think this is your best bet, but who am I.
I don't have to say why this is a good idea, the arguments are explained in the question already.
Given my design ideas, the user won't lose the preview option he has now (just the new text). The design idea I gave only adds features, without really changing an existing feature.