I'm not sure what you mean by "academic." If you mean "intense and intellectually rigorous" then yes. If you mean "similar to work done at a university" then not really.

Most charedi men's Torah learning is Talmud, or as it's more commonly called, Gemara. While both boys and girls will start learning Tanach (the Bible) in first grade, by about third or fourth grade boys will add Mishna to their daily learning- the core material of the Gemara, which is also easier for younger children to learn as it is in Hebrew. By about fifth grade, they begin learning Gemara- this requires learning many words in Aramaic, and is much more complicated than learning Tanach or Mishna alone. It is basically taking the halacha (Jewish law) which is explicated first in the Tanach and then in the Mishna, and bringing together many rabbinical arguments, esoteric discussions, and abstruse comparisons. While in theory these arguments are meant to resolve and explain issues, it's not uncommon for an issue to be explained in completely different terms in two different sections (masechtos- there are 63 of them). The fact that this is all so complex means that Gemara is always studied with two different commentaries- the 11th century commentary of Rashi, Rabbi Shlomo Yitzchaki, which explains difficult words and ideas; and the 12-14th century commentary of a group of rabbis called the Tosafists, who wrote massive works, later compiled into a more streamlined commentary called Tosafos, which attempt to reconcile all of the places where a topic is brought up multiple times in the different masechtos. These commentaries are so important that in nearly every edition of the Talmud, the Mishnaic and Talmudic text are in the center, Rashi's commentary is on the outside, and Tosafos are on the inside. That's not the only thing that's used- there are literally hundreds of commentaries written over the last thousand years, many of which are still used today. By and large, by the time an Orthodox Jewish boy reaches high school the majority of his time learning Jewish subjects is spent on Gemara. In charedi schools, this may be nearly all of his time. Many boys continue learning Gemara full-time for at least a year or two after high school- for charedi boys/men, this can actually continue for many years.

I want to emphasize that while Gemara is definitely a major part of Jewish law, the main goal in its study is NOT the actual elucidation of the laws, or halachos. Learning halacha for practical reasons is usually not the major focus of a boy's Judaic education, for whatever reason. While halacha certainly comes up as part of Gemara learning, it is not the focus and the idea is that this Gemara learning should be for its own sake, even if its on a topic which has little relevance in daily life. The average Gemara shiur (lecture) is more interested in exploring six sides of a halachic issue than in actually revealing what the practical halacha is at the end of the day. The focus is on the intellectual debate and a very legalistic way of thinking. The particular way in which Gemara has been learned over time has certainly changed- but the current dominant method is influenced by the "Brisker" method (named after the town in Poland from which its founder originated), and is noted for its very logic-based and conceptual approach. This study can be extremely rigorous and intellectually demanding, and in that sense it is certainly "academic."

However, in other senses, Gemara study in yeshivos (Jewish schools, often specifically used to denote those devoted to Gemara) is quite different than typical university study. For one thing, the way in which it is studied is quite distinct- students learn in pairs, or chavrusos, in the beis midrash (study hall), and then only afterward are they gathered together for lecture, which presumes at least some mastery of the material. The chavrusa method is a key part of Gemara learning and has been for hundreds of years, as the back and forth (sometimes called the "milchamta shel Torah," or "war of Torah) is considered to help students fully understand the topics being learned. Generally, there are no real classes in the sense that there would be in a university- there may be tracked shiurim, in which the most intelligent and advanced students attend the shiur of the leading rabbi at the yeshiva and so on down, but usually the whole yeshiva will learn the same masechta of Gemara, though there will often be secondary times of day or breakaway groups to learn other topics. Since the aim is all about the journey and not the destination, unless a student is specifically studying for rabbinical ordination (in which case there are many specific topics of halacha which must be covered), the aim is not to learn specific topics or a given number of topics- it's to learn whatever the yeshiva as a whole is learning.

Generally, the form of publication favored is that of sefarim, or books- to publish a sefer is considered a high point in a rabbi's career. While there are journals, they are not considered as significant and are usually more favored by younger scholars. While a rabbi may develop a particular expertise in or interest in a given area, this is far from the equivalent of a professor who did a thesis in a particular topic- it is rather just a part of an overarching knowledge of all of Gemara and its commentaries. They are not learning in order to publish for practical reasons, but because it is seen as an inherently positive thing to do. Learning Torah (in the overarching sense that includes Tanach, Mishna and Gemara) is considered to be a mitzvah (commandment) in its own right and to have great spiritual benefit. For this reason, in most post-high school yeshivos there are no exams.

Most of the above, for the record, applies to all Gemara study- but I will note that there is something of a leaning in some non-charedi circles toward a more academic approach to Gemara- in the sense of putting it in its context in history, applying critical methods, etc. This is not something done in charedi yeshivos, which prefer to focus on learning Gemara on its own terms.