No but you do say "I'm diabetic" which uses diabetes as sort of identity within the sentence structure.

Similarly "I'm a cancer survivor" and "I'm a cancer patient" are ways someone with cancer could structure a sentence to give weight to the way cancer and the experiences of cancer fundamentally change this person's personality and identity.

While "I am ADHD" isn't perfect, it's a very new use of language to try and create an identity form, and it will continue to evolve and sound more natural.

Personally I still find myself saying "I'm autistic and I have ADHD" in most situations, but if I know I won't have to explain the term too much, I do prefer "I'm AuDHD", because it's an identity first phrase, and it feels as natural as "I'm autistic" or "I'm diabetic".

But the difference grammatically between "I'm autistic" and "I'm ADHD" is minimal, yet I agree one sounds fine and the other just sounds stupid. And other than exposure, I can't place my finger on why.