This question seems to be based on a few false premises.
As KarlG points out, "acediast" doesn't seem to have ever been appreciably more common than it is presently, so it doesn't seem right to describe it as an "archaic word" (a description that implies that it was once more common than it is today). (The formation, as opposed to the specific word, does seem to have existed since Ancient Greek: Liddell and Scott's Greek-English Lexicon has an entry for ἀκηδιαστής (akēdiastēs). There are also a few examples on the web of parallel forms in other languages, like acediaste in French and acediasta in Portuguese, although I was only able to find examples of these in documents from recent years.)
Furthermore, whether a word is archaic or not is only one factor out of many that will affect whether a reader can understand it. The word "thou" is archaic, but almost any English speaker will understand what it means. The word "noetic" is not archaic, but many English speakers will not understand what it means.
Since there is no official specification of the English language, there is no authority that can prevent you from using difficult-to-understand, archaic, or even newly invented words in your writing. But depending on what the author's goals are, it might be wise to avoid doing that. That's a matter of writing advice, though, and so outside of the scope of this site.