Is use of the word "via" appropriate in an academic essay?
There is nothing wrong with the word "via," and in fact I personally have a weakness for it: sometimes it just feels more elegant and specific than alternatives like "through" or "by means of."  I also, however, have a weakness for a lot of somewhat archaic phrases, due to spending a lot of my childhood reading old books.  

The general principle which I think academic writing should subscribe to is Orwell's notion of "transparent prose," in which the words are as clear as a window, letting one through to the ideas with minimal obstruction.  Using too many unusual words, such as a lot of "via" and "thus" can be distracting, particularly for an international audience.  Sometimes, though, a word is simply fit and elegant in its context, and there is no reason to avoid using it.