Some thoughts:
Java EE 6 is not wide mainstream now, but some knowledge might still be useful. Example (IMHO):
Servlet API, JPA.
Java EE 7 exam - extremely difficult, I took it only because passed all (except
JSF) Java EE 6 exams earlier, and it helped a lot.
There is some exam about Java EE from RedHat, consider it as option.
OCM (architect) does not have any pre-requisite to take some exam. Not sure when OCM exam updated, but suspect it valid against Java EE 6.
If your aim is OCM - I would recommend reading books recommended here, do not bother with Java EE 7 exam, and proceed to OCM directly.