The exam objective related to this topic is the following:
Section 10: Building a Custom Tag Library Given a scenario, write tag handler code to access the parent tag and an arbitrary tag ancestor.
It doesn't explicitly say that the TagAdapter is part of the exam, but it is good to know how it works. You will probably never write your own TagAdapter class unless your are involved in servlet-container development (the container will create the class when it sees that the parent of a Classic Tag is a SimpleTag)
For your information, I didn't get any questions about this on the exam though.