"Fugue" is a noun. It is never genuinely an adjective. All the very thoughtful answers here which attempt to create a metaphorical description of a person as a fugue are creative and interesting, but they don't really answer what I take to be the question at hand, namely, can something be described as "fugue?" In other words, is "fugue" usable as an adjective? For example, could you say, "She was a fugue girl?" Again, I say no.
Is "fugue" nevertheless used as an adjective? Sometimes, yes, but it is used that way almost exclusively as mentioned in some of these answers, that is, in conjunction with a state of mind. My opinion is that this usage, "fugue state," occurs because of a tendency to want to clarify "fugue," which is something of an unusual term, even in medical contexts. It is entirely appropriate and correct to say a person entered a fugue, but it is understandable that this "feels" inadequate merely because the word is uncommon. So although a fugue is indeed a state of mind, the word "state" is often (redundantly) appended to it.