Is it possible to outrank an .edu domain?

Yeah, I've been wondering about this.

For example: harvard.edu
Then lets say you start a website: HarvardRocks.com

Is it possible to outrank harvard.edu with your "Harvardrocks.com" for the anchor name: "Harvard University" ?

possible? yes. likely? no. will harvard send you a C&D for using their name in your domain? definitely.