In a word, yes. You can have a mental disorder that co-exists with GID.
When I was 20, in 1970, I was living part time male, part time female. I had been having serious issues from the age of 5 or so, was mostly raised as a female well into my teens, and was starting to lose track of things to the point of (almost) really believing that I was born genetically female. In other words, I was worried that I was, or was becoming delusional.
GID, is unfortunately, something that colors all aspects of your life, and invites confusion and difficulty all across the spectrum. The problem is enhanced by the difficulty in recognizing when to find help. People who have no REAL understanding, are of little help, and the attitude of "if I can't see it, it doesn't exist," is too prevalent.
GID is truly a potentially debilitating condition, and it can bring with it a host of associated problems that require a knowledgeable and skillful practitioner to sort it all out. That may be part of the thinking behind the requirement in the Standards of Care, that one of the letters recommending SRS is from a therapist specializing in gender related concerns who has a Phd., so that the client can be evaluated for comorbid problems prior to SRS.