There are a few things to consider here. Firstly, Buzz only works if you are a Gmail subscriber. While this may well be a massive number of users, it could also draw in many more users as a result. It's not necessarily designed to be a Twitter or Facebook replacement or substitute, rather something amalgamated from the two existing services to better serve the Google user.
But at the moment, the Google vs. Microsoft battle for university productivity and email services is taking out campus by campus like a Wild West shoot out.
More universities are opting for the Microsoft solution than the Google solution, meaning more students are using Live@edu and the Outlook Web interface for university email and file sharing, while Google takes on the secondary, personal accounts.
Google Apps users may not necessarily have access to Buzz just yet, but anyone with a Gmail account can play with it anyway. Google will be widening Buzz to include it as part of their Apps education suite which rolls out to the minority of universities and colleges which go with it.
For Live@edu users, who have in-built messaging capabilities to other Live@edu users will have to suffice. What Buzz is to Twitter, Live@edu is to Facebook chat.
I don't think for a minute Buzz will have any major effect on the non-Google world. Twitter for work and for fun, along with personal Facebook accounts will keep far more different kinds of people connected without the barrier of needing an account to have a single peek.