In the College (and I believe the other schools as well, but I am not as sure about them) a minimum of two semesters of Theology are required. The first course must be either "The Problem of God" (taught by many different professors so each section has its own spin) or Introduction to Biblical Literature. For the second semester students may choose an intermediate-level elective; there is quite a broad range of these, so while many students choose to focus on Christianity a/o Catholicism, many others study other world religions or a variety of religions.
I was one of the Georgetown University students graduating two weeks ago when Cardinal Arinze delivered his speech.
To clarify - yes, the "mocked by homosexuality" line was read at the ceremony. Moreover, the text of the speech posted here is incomplete - my suspicion is that the copy sent by the Dean was a draft rather than a transcript. The Cardinal expounded upon issues of homosexuality, divorce, and premarital sex to a degree that is not reflected in this version of the speech.
A large percentage, if not the majority, of the graduates at that ceremony had probably read _Nichomachean Ethics_ during their time at Georgetown. Many of Georgetown's professors of philosophy and ethics - and all of the best of these professors - include NE on their syllabi. When reviewing Georgetown's incorporation of and emphasis on ethics, it is important to note that the University consists of four distinct schools (Arinze spoke at the commencement for the College of Arts and Sciences; the other schools are the Business School, Nursing School, and School of Foreign Service), and that each of these schools have their own requirements. In the college, it is required that all students complete a minimum of one course in ethics and one philosophy course.