I have a story I want to do that involves my sims being college students, and as such, I want them to live in the university world indefinitely.

Furthermore, is there a way to make everyone in the university world stay there indefinitely?

In theory, you could travel your first household to Uni World as if on a vacation, meaning don't enroll at Uni from the homeworld, have them purchase and move into a vacation home, invoke Travler's Change Hometown on them thus making Uni World their hometown (upon a save, total quit, and reload), and then get other sims and households left behind to join by way of MasterContoller's Add Sim > Homeworld (filter to original homeworld).

In practice, Uni World isn't very conducive to gameplay as a homeworld and different players will have different levels of success with this. And I'm not sure about the transiency of the other Uni Students who aren't town residents as that's just the way Uni World is designed to work.

It may be more work to set up in the beginning, but I would suggest considering a different world for this project, either a custom one that looks like a college town or one of your own design that does, and deploy a Homeworld University on it by way of the Careers mod. Then when all is said and done, Uni Student (Level 1) and Uni Professor (Level 2) become local careers without all the overhead of traveling back and forth and without the transiency of other students.