Occasionally some do. I know many of them learn it just to become familiar with some of the grammar, lexical variants, and such. It makes more sense for a New Testament scholar to do so, given that the Hebrew Bible was written before Arabic was widely spoken. In fact Old Arabic isn’t even attested in writing until the first century CE, in the Nabataean Script.

I know a few scholars of Hebrew Bible, like Dr. Anthony Tomasino, learned some general basics of Arabic. But beyond that it isn’t particularly common for them to become outright readers of it. Most of them who know Arabic use it for the lexical variants and finding cognates, hence why it is referenced often in Hebrew Dictionaries. However, most scholars of Hebrew Bible that I know of do not learn it anywhere near the extent to which they do Latin, Greek, Hebrew, Syriac, Aramaic, Ugaritic, German (which is what a good chunk of Biblical scholarship is written in now), and even Akkadian (as that language is highly important for reading ancient Cuneiform scripts, which often serve as literary parallels for Biblical writings).

I, myself, though not a scholar (but am pursuing my PhD in Hebrew Bible), will probably not be learning Arabic to any large extent. My focuses at the moment are learning Hebrew, Greek, Latin, and Aramaic.