But then it wouldn't be functioning as an adjective in the sentence, would it?
Adjectives are descriptors. So what does the word "trans" describe in this context?
If you put the adjectives "tall", "short", "fat", "thin", "old", "young", "black" or "white" in front of the word "woman", we have a clear understanding of what characteristic of the woman is being described.
Not so with "trans", which is, as another poster mentioned, a prefix.
At best, you could argue that "trans" as an adjective is short for "transgender", meaning someone whose gender identity does not align with their biological sex.
But there are two problems with that.
Firstly, there is no clear definition of what a gender identity is or how one can align or not align with either biological sex, which is a completely different thing. You're describing trans people as people whose identity does not match their biological sex, but in my view this does not explain how trans people are materially different to non trans people.
And secondly, even if you accept that the feature you are describing is having a gender identity which does not match their biological sex, "trans" or "transgender" only functions correctly as an adjective if it is attached to a noun which means the same thing when different adjectives are attached to it.
For example:
tall + woman = female person of above average height
short + woman = female person of below average height
black + woman = female person with very dark skin
white + woman = female person with pale skin
Logically, then, if we follow the same pattern:
trans + woman = female person with a gender identity which does not align with their biological sex
But no. It doesn't mean that, does it? It means male person with a gender identity which does not align with their biological sex.
So "trans" cannot be properly said to be an adjective here, because adjectives describe nouns, adding context to them, whereas the function of the word "trans" here is to change the meaning of the noun, creating ambiguity.
"Woman" has to mean "female person". It cannot mean anything else, because if it meant "person with a particular gender identity", trans women would not need the "trans" part, because the noun "women" would already describe them without needing an additional qualifier.
And if the word "woman" has to mean "female person", in order for "trans" to be an adjective, "trans woman" would have to mean "female person with a gender identity which does not align with their biological sex".
If it doesn't mean that, "trans" is not functioning as an adjective in any sentence containing the words "trans women".