I would agree with the advice given that it's OK to jump into J2EE from learning core Java. That said, I would continuously hone your core Java skills.
When I'm looking for J2EE developers that I want on my team, I look for folks that know how to write simple maintainable code by exploiting the JDK to its fullest extent. You should know the collections API like the back of your hand. You should definitely practice the advice given in Effective Java. Eventually you will have to know some of the subtleties of threading (step 1: keep your objects immutable; step 2: see step 1).
BTW, if you're in the New York area, leave a comment and maybe we can contact each other offline.
Clarification: every interesting Java application will require business logic and the use of plain old Java objects (POJOs). Trivially, that includes J2EE applications, whether it is a web app, a framework for use by web apps, or even a J2EE app server itself. It's usually an eye opening experience for a Java developer once they've developed a "toy" app server. J2EE becomes a lot easier after that.
By my lights, a true J2EE "Jedi master" knows how to take apart an app server to its basic core Java components. E.g. EJBs are proxies that wrap business POJOs by adding the capability for remote procedure calls with the RMI networking protocol as well as a transactional manager. If you understand RPCs, RMI and transactions, your chances of understanding EJBs rapidly goes up.
Or to put it in Joel Spolsky talk, J2EE is a leaky abstraction built on top of the J2SE networking API.