Final answer:
The statement that adverbs not ending in -ly should be hyphenated when they precede a noun to form a compound modifier is true. When such modifiers come after the noun, they are not hyphenated. This does not affect adverbial modifiers which usually modify verbs.
Step-by-step explanation:
The rule stated in the question suggests that adverbs not ending in -ly should be hyphenated when used as compound modifiers in front of a noun, which is true. For example, 'well-known author' and 'chocolate-covered peanuts' show that when such compound words precede a noun, they should indeed be hyphenated. In contrast, when these combinations come after the noun, the hyphen is not used, as in 'the author is well known' or 'peanuts that are chocolate covered'.
It is also pertinent to remember that if each word operates separately to modify the noun, they should not be hyphenated. Additionally, when we speak of other grammatical elements such as adjectives and their modifiers, it's worth noting that they do not always need a hyphen unless they form a single modifier before a noun, contributing to the clarity of the sentence. Lastly, these same principles do not necessarily apply to adverbial modifiers, which often (but not exclusively) end in -ly and are used to modify verbs.