Eating Disorder...NO

But that's not to say that Sherlock's eating habits are regular.
"Don't eat when I'm working, digestion slows me down."
The Blind Banker - Sherlock Holmes
Which is a paraphrase of Sherlock in literature.
"Because the faculties become refined when you starve them. Why, surely, as a doctor, my dear Watson, you must admit that what your digestion gains in the way of blood supply is so much lost to the brain. I am a brain, Watson. The rest of me is a mere appendix. Therefore, it is the brain I must consider."
The Adventure of the Mazarin Stone - A Conan Doyle
He does eat though..
There are instances of him actually eating or talking about it.

Last 2 images from The Norwood Builder (others also there)