nouns - Is a dark polka dot necktie dark?

In The Syntactic Phenomena of English, McCawley considers the phrase "a dark blue necktie", and concludes that "blue" in that phrase is simultaneously a noun and an adjective. It modifies the noun necktie, so it must be an adjective, but it must be a noun also, since it is modified by the adjective "dark". If "dark" modified an adjective "blue", it would have to be an adverb "darkly", since adjectives can't modify other adjectives.

But a skeptic might wonder whether "dark" actually does modify "blue". Maybe, instead, "dark" modifies "blue necktie", and we are simply dealing here with a noun "necktie" modified by the two adjectives "blue" and "dark". The problem with the example arises because a necktie colored dark blue will always be dark, itself.

So let's look for a less equivocal example. A "dark polka dot necktie" might have dark polka dots yet still fail to be dark, because although each individual polka dot was dark, if the polka dots were small and on a light background, the polka dot tie as a whole might be light, rather than dark. In that case, "dark" cannot be modifying "polka dot tie", so it would have to modify only "polka dot".

So, if a dark polka dot tie is not necessarily dark, then McCawley's analysis must be right. Is it?