Is it common for Jewish scholars to study Aramaic?

No, absolutely not, except for a small group of scholars who do study Aramaic.

Does the average religious Jew have any interest in learning Aramaic?

No, absolutely not, not as a language per se, although incidentally as a student of Talmud such a person will know and understand some "Aramaic" words and phrases.

Let's understand the difference between "studying the Talmud" and "studying Aramaic." The Talmud is written in Aramaic, so you would think, to study the Talmud I should first study Aramaic, right? Wrong, because the Talmud is not written in spoken Aramaic, it's written in a legal jargon of Aramaic with a limited vocabulary. That is, certain stereotyped Aramaic words and phrases that express legal ideas and patterns of argumentation are used over and over in the Talmud; but no-one spoke like this back in the day or since. Hence "studying Aramaic" is not really the key to understanding the Talmud; understanding the legal jargon is the key, the way arguments are phrased and resolved. This is learned, not by formally studying Aramaic, but by studying the Talmud itself, so that the typical phrases and usages (tanya, kah mashma lan, havi amina, tanna kamma, tanna basra, teiku, tannu rabbanan, reisha, seifa, etc.) are learned and understood. Talmud students, who understand the Talmud perfectly, receive no instruction in Aramaic per se, and couldn't speak a sentence if their life depended on it (which it doesn't). By contrast, a small group of scholars -- in universities, not yeshivot, who have Ph.D.'s, but not necessarily semikha (ordination) -- who are linguists by training and inclination, do study Aramaic of the Talmud, relate it to other dialects of Aramaic and Semitic languages and publish their findings in monographs and dictionaries.

Lots of Jews have some familiarity with Aramaic, from its close relationship to Hebrew, from the Bible (Daniel, Ezra-Nehemiah, Daniel), from prayers (kaddish, yekum purkan, Akdamut), from the Talmud and from the Zohar. But systematic instruction in the language? Nil.