Learning Java SE is not only learning to develop desktop applications or applets (which are basically just Swing/AWT). You learns how to use and write basic Java code and to make use of the basic Java SE API's. You still need them in Java EE. You'll need to write plain Java SE code in the Servlet methods, the DAO classes, the domain/model objects, etcetera. In practically all classes which you need to implement/create for Java EE.
So yes, I can strongly recommend to learn Java SE first, if not done yet. Sun has nice tutorials about that, check the chapter Trails Covering the Basics. If you prefer a book, then I can recommend the Head First Java and/or maybe the SCJP6 book of the same authors. You can however skip any Swing/AWT chapters. You don't need to know about them in Java EE.