The New Oxford American Dictionary defines one sense of drag to be:
Clothing more conventionally worn by the opposite sex, esp. women's clothes worn by a man: a fashion show, complete with men in drag | [as adj.] a live drag show
Now that second bit saying that it is an adjective raises my eyebrows a bit, because that example doesn't look like an adjective to me. I parse that as
a live drag show det. adj. noun compound
And I feel this interpretation is vindicated if we contrast sentences like
The show will be so extravagant.
*The show will be so drag.
Here I replaced an adjective (extravagant) describing a "show" (the same noun in the sentence provided by the dictionary) with "drag" and got a sentence that seems to me to be ungrammatical. If "drag" were being used as an adjective in the example sentence then it should be separable from the noun it modifies, and it seems to not be. And this evidence is completely congruent with a noun compound understanding of the phrase.
Now to be a little less naïve, I do definitely see how one could think that drag is an adjective in the sentence. My perspective is quite different from a monolingual English speaker who did not spend a large amount of time in school diagramming sentences. It is a word right before a noun that modifies it, which is basically how adjectives work most the time. And I could definitely see it being a pragmatic choice on the part of the dictionary to cater towards a simpler more approachable understanding. However the issue I see with this is that English allows noun compounding with basically all nouns. And the NOAD does not list every noun this way. So there must be something special about the word it is trying to tell me, but I don't know what it is.
So my questions here are: What's going wrong? Have I misread the dictionary? What is the dictionary trying to tell me.