Where and when should a monogram be used?
In some cases the monogram can be used for the favicon image.
You can also use it on letterhead as a watermark or as background patterns on some other projects.
You can use it for stamps, pins, seals, badges, or stickers.
It can be use as a nice subtle embossing or spot varnish on a business card, or high budget print project.
There's so many ways to use it or create concepts based on it that it's actually nice to have one. As for mascots, a tagline or anything that is part of the identity of a business, the monogram will also end up being associated with it at some point.
It's by using it that the audience will know that monogram is associated with the College. It doesn't really matter if the monogram doesn't look 100% related to the logo. You can think of JRR Tolkien monogram for example. You'd show it by itself to people who know nothing about him, they won't even know it's his "seal" or even see the letters in the monogram. Even 15-20 years ago, way less people than today knew about it, only the "exclusive fans" did. But if you show it to his audience now, they don't need to be told it's the JRR Tolkien signature/monogram, they saw it on the Hobbit cover, movie posters, magazines, etc. There was some brand recognition work done over time and exposition to that symbol.
When should you avoid it?
You shouldn't use it for the sake of using it!
For example, you asked if it should be used with the logo and if it won't be redundant: well you got a point, it might be too much unless you succeed in incorporating it somehow as a badge or something.
But it shouldn't be used all the time if possible; only if it adds a nice touch to the design or if it's necessary. A monogram can be considered a bit like the abbreviation of a logo and in general, you don't need to use the whole logo and its "abbreviation" at the same time.
It's possible your client/college/managers will demand you to use it everywhere and every time because some people are like that... You'll need to either try to give them the "abbreviation" explanation to be able to have the freedom to use it or not, or you might need to find creative ways to incorporate it as patterns or watermark-style to please them.