Yes, absolutely. There are plenty of descriptions of this in various grammars.
Recently, I have been thinking a lot about the pretty arbitrary nature of what we usually call "parts of speech" (see this article
for some of my more obscure thinking if you can bear it). One insight has been that the accepted categorizations of pretty well all parts of speech are rarely tenable, at least from a functional point of view. The concept of adverbs in particular seems to me to have been thoroughly abused over the years.
My thinking led me to the conclusion that "true" adverbs, irrespective of the form they take (i.e. with or without "-ly"), identify an aspect of an action (generally a verb) that fundamentally changes our conceptualization of the action. In other words, if we say "he walked along the road", we have a mental image of a man walking, and if we say "he walked along the road quickly", this mental image changes. Many adjuncts are also referred to as "adverbials", especially those referring to time, but as I see it, the time expression in "he walked along the road in the morning" in no way changes our mental image of the act of walking (nor indeed does "along the road"). This seems to contrast with adverbial expressions of manner, which do change our mental image: "He walked along the road with some urgency".
By that line of thinking, "hardly" is a true adverb (although it is unrelated in meaning to the adjective "hard"), while "hard" in the collocation "hard boil" is not a true adverb. In contrast, however, the "hard" in "he hit the ground hard" does change our mental image of his making contact with the ground, and is a true adverb.
In reality, of course, both "hardly" and "hard" in the case in hand are special cases. While "hardly" can be seen as a true adverb by my definition, it does not behave in the same way as other adverbs (you cannot say "he boiled the egg hardly"). And the resultative meaning of "hard" in "hard boiled" is only found preceding the verb in a few set expressions such as "hard boiled" or "hard done by". Otherwise, it tends to follow the verb, as in "frozen hard".
Sorry. My head is at the moment full of questions like "why can we say things like 'thick-skinned'", and it spills over into my posts. After all, "thick" is not an adverb, true or otherwise, and "skin" does not exist as a verb in this meaning except in this expression. And ...