I've not done what you envision, but sure. It's not far-fetched. How seperated do you want? If you want complete seperation of the 4 areas, then you might as well have 4 installations. So I'm assuming you want SOME integration between the 4. What are your ideas?
I've not used vBulletin, but I hear it is very nice. phpBB is of course very nice and popular, and the biggest selling point (misnomer), it is free.
I can think of one great reason to have it be a single board system for all 4 forums is that way people could have one account, but be members of multiple "forums".
Most forums already have a built-in, simple method to have multiple forums. For example, go to
http://www.geekweekonline.com/forum. It's a website run by a strange friend of mine. I host him. What you'll be looking at is a phpBB system. Notice the main sections:
Announcements and Site News
General
Gaming
Tech Center
The Arts
You could use those top-level categories as your various forum sections. It would not be too difficult to then color code them, but that would be a hack.