If my College is teaching me JSE rather than
J2EE does this make me less
employable?
No. That's what your university should do: focus on fundamentals. In the case of Java, that mostly means the standard edition.
Java EE (not J2EE; see my comment in the question) adds some server-side Java APIs, specifications and libraries. The most important of these are the Servlet API and JSP container specification. But I think it's important to know that even on the server side, it's still mostly about standard Java! It's quite possible that you'll do server-side Java development without ever needing to learn most Java EE technologies, like Enterprise Java Beans (EJB) - especially with the rise of alternative, lightweight approaches such as favouring POJOs, with Hibernate for persistence layer. Many parts of Java EE like EJB have definitely long passed the peak of their hype cycle. You may not even need to know all "lower-level" Servlet and JSP stuff thoroughly, as higher-level frameworks such as Struts, JSF, or Wicket have become popular.
One case study: I learned fundamentals of Java (and OO programming) at the university - and only very little (and nothing practical) about the Enterprise Edition. Now I've worked some 4-5 as "Java EE developer", that is, doing server side Java. I've never really used EJB, or most other Java EE technologies. I've mostly done just pure Java (i.e. standard edition), with some JSP, Servlets, Filters, etc related stuff thrown in (plus of course web techniques like HTML, JS, CSS); making use of lots of (mostly open-source) 3rd party libraries, and picking up everything as needed. (However, I am planning to brush up my knowledge of Java EE, and take the SCWCD at some point - I think that would do me good even if JSE goes a long way :)