Can I write the diversity statement around my ADHD?
Look around, but I think @Anonymous Physicist is right that this isn't about you but about how you will handle diversity in your interactions with the university community you are likely to encounter if you are hired as a PhD student at this school (and maybe as a Teaching Assistant (TA)). See, for example, Vanderbilt's Center for Teaching's definition of what their Diversity Statement expectations are.
In that case, I would say that you should weigh your own personal experiences as a person with ADHD against others who are different races or from other countries or ... against what you have experienced before bringing it up. It's unlikely to be considered relevant, in my opinion.