Hi,
I believe Enterprise application development is what you meant by "advanced java". If your requirement is learning EJBs, having a good experience with java SE will be a good to start learning Java EE. And since you have little knowledge on servlets and JSPs(for presentation tier), that would definitely help for a complete picture of the java EE and for your
testing purposes during your learning of EJBs.
So, you can definitely go ahead with learning EJBs. And I recommend EJB3.0 in Action which I found as a very nice guide for starters.
And you can move this to the EJB forum, participate and post your queries related to EJBs in that forum for further help with your EJB learning.
The book also covers concepts related to persistence(saving data to db) and the specification(JPA). JPA is similar to what Hibernate framework implements and hence you may choose not to learn hibernate separately.
My career is also in similar lines.. so all the best