From my personal experience from learning Java EE/Web programming from the just standard Java, I tried to jump right into some of the frameworks without a clear understanding of how the Java EE/Web stuff worked. While not all of Java EE is relevant if you are using a framework like Spring, I think it is a good idea to have a good grasp of some of the underlying technologies. You don't have to go overboard, but understanding some of the basics is a good idea.
When something is not configured correctly in the libraries (like Spring) sometimes they assume a certain level of knowledge on their user's part. After struggling with a few basic issues, I spent some time and went back to the basics. After that I was better able to deal with the frameworks.
I would just forgo the EJB route though.
