Whether or not your campus supports Linux is a moot issue. As long as all their equipment is standard, you should be fine. The way to be sure is to just bring your Linux laptop to campus during the tour and try connecting to campus WiFi, etc. Also, look up security policies, class syllabi, etc. to ensure that there aren't anything Windows-specific.
Truth is, most professors don't care how you got something done, as long as you got it done properly and honestly. In many humanities classes, I've typesetted my papers in LaTeX and often became the only person whose papers aren't in MLA. Even then, nobody complained -- it was all about the content. Then, if the professor was really fussy, you can always use a package that formats your paper MLA and makes it basically indistinguishable from a Word document.
In fact, the only department that will probably notice that you weren't using Windows / Mac is probably the CS department. In that case, there will probably be better support for Linux anyways.
Point is, if you want to use Linux, you can. However, it's difficult to provide support to all the configurations, so if you can't set up everything based on OS-neutral instructions, then you should either get a geek friend to help or just use Windows / Mac like everyone else. Windows-specific app? No problem, virtualization is the way to go.
