Wheaton had a more Protestant emphasis than our OP is looking for -- I assume he wants less of Luther and Calvin, more of Thomas Aquinas and the Western Fathers -- but I think that a theology professor at a Catholic school will be teaching classes that are otherwise similar to what I saw at Wheaton.
I think so.
Vatican II had a few things to say about the training of priests, and being a theology professor, one would be, among other things, training priests. So you can't teach what you don't know.
From Dei Verbum, about the need to be soaked in Scripture:
24. Sacred theology rests on the written word of God, together with sacred tradition, as its primary and perpetual foundation. By scrutinizing in the light of faith all truth stored up in the mystery of Christ, theology is most powerfully strengthened and constantly rejuvenated by that word. For the Sacred Scriptures contain the word of God and since they are inspired, really are the word of God; and so the study of the sacred page is, as it were, the soul of sacred theology.
As the soul of sacred theology, the Bible is obviously key. One would expect a professor of theology, even a professor of moral theology for example, to be deeply Biblically literate, presumably knowing well at least Koine Greek, if not Hebrew and Aramaic. A professor of theology focused on Scripture would also maybe be an expert on other ancient languages like Ugaritic. But no way around it that one would have to master Koine Greek. That's my opinion, but the council itself calls for Scripture at the core of theology, and I don't see how one can be expert in Scripture and not know the languages.
From Optatum Totius, about the training of priests:
13. Before beginning specifically ecclesiastical subjects, seminarians should be equipped with that humanistic and scientific training which young men in their own countries are wont to have as a foundation for higher studies. Moreover they are to acquire a knowledge of Latin which will enable them to understand and make use of the sources of so many sciences and of the documents of the Church. The study of the liturgical language proper to each rite should be considered necessary; a suitable knowledge of the languages of the Bible and of Tradition should be greatly encouraged.
Here it's clear that Latin will be important for someone doing Catholic theology. Maybe not for a Protestant, but indeed for a Catholic. One of my books is by Bernard Lonergan, a textbook of his that he used while teaching in Rome. It's entirely Latin. In that way he could teach to more than just Americans, Canadians, British, Australians, and New Zealanders. Latin was, and to a considerable degree still is the language for Catholic theology. Someone who plans to be a professor of Catholic theology needs to know Latin.
As I mentioned before, Latin and Greek have some similarities, enough that leaning them both at the same time is a good idea. Someone else mentioned that it would be beneficial to study Classics, that is Greek and Roman literature. I agree. A Classics department minor might be the way to go as an undergraduate.
As to which language is more important, I'm presuming that it does not boil down to ONE language. Several will be key. Greek for sure. Latin for sure. Probably Hebrew and/or Aramaic. Maybe other ancient languages. Probably a major modern European language or two. I'd go with Italian, but German and Spanish and French could be valuable too. It depends on where you want to go to study. You definitely should get out of the country for that at some point for a few years if at all you can. And that's where I mentioned the Pontifical institutions. A diversity of institutions, one for Masters, another for doctorate, another for post-doc, provided they all are of good reputation, will assist you on your path. It's an arduous path. But even if you bail out part way, you have learned some very good stuff. Just get wise counsel along the way to plan your way.
