Without giving it a whole lot of thought, and also without completely understanding your user breakdown, yes it should be more than possible using a combination of user groups and categories.
I would also strongly advise you to sit down and think very carefully about your security model before you go ahead and implement. While you will have the flexibility to change that model ad-hoc, having a clear indication of how you would plan to go about creating the security model will save you some headaches in the future.
On the face of it, I think at the most basic level, I assume a College can have multiple campuses, so you can create a user group for each College, with Campuses as subgroups.
Categories could be use to manage things such as clubs, such that individual or multiple campuses could have access to club material (wiki docs, forums etc.)
I'm inclined to not create user groups for clubs but I can't really give a good reason why at the moment except to say that depending upon how many clubs you're talking about user maintenance could become a complete nightmare. How do you intend to keep track of which individual users belong to which clubs? It's probably easier to keep track of which campuses are able to utilize which clubs.
Note that users can belong to more than one user group, and that user groups can be hierarchical (sub-groups as you mention).
I think to help you further we'd really need a much better understanding of your particular needs since there are many possible solutions, some better than others.
Update Just to tack on a little after-thought I had, Tiki also has an "Inter-Tiki" feature that lets you seamlessly work with multiple Tiki sites but I haven't used this, nor do I know its current state of functionality or operation, but it might be something else worth considering if one site ever got too large or unmanageable.