For faculty candidates with history of severe mental illness, would a Diversity statement be an appropriate place to raise those issues? Could such a candidate bring a unique background that could be valuable to an organization?
Note: this answer was written when the question was framed as "someone with severe mental illness", not "someone with a history of drug abuse and suicide attempts".
It would depend on who was evaluating your statement! It's pretty easy to find support for the view that disability is considered (by some) a component of diversity, e.g. from the (Canadian) Social Sciences and Humanities Research Council:
Diversity is defined as differences based on factors such as, but not limited to age, culture, disability, education, ethnicity, gender expression and gender identity, immigration and newcomer status, Indigenous identity, language, neurodiversity, parental status/responsibility, place of origin, religion, race, sexual orientation, and socio-economic status.
And also that mental illness is considered (by some) a form of disability, e.g. from the Ontario Human Rights Commission:
The duty to accommodate mental health disabilities is no less rigorous than the duty to accommodate physical disabilities.
My own two cents: whether having a mental health disability counts toward EDI (equity, diversity, and inclusion) will depend on who is reading your statement. Some people evaluating diversity statements value "personal" diversity (i.e., you are a member of an underrepresented/equity-seeking group), and some want only to know how you will improve outcomes for members of underrepresented/equity-seeking groups. Think carefully about the different reasons that EDI is valued, and articulate which ones/why you think they are important. Don't say "I have mental illness, therefore I am deserving of a position" (this is deliberate exaggeration on my part); instead, explain why your mental illness improves equity, diversity, and inclusion, and why that matters:
- diversity to improve research outcomes: perhaps your mental illness (and, hopefully, having overcome/managed it) allows you to bring a different perspective to problems
- representation: if you are open about your mental illness, that representation (i.e., knowing that someone with mental illness can succeed in the field) could encourage participation by/success of students who have mental health issues
- improving outcomes: your experience with mental illness could give you an advantage in helping students with mental illness succeed
Frame challenge: Your question implies you don't understand mental illness, nor suicidal ideation, nor drug abuse, nor diversity
Drug abuse is not a mental illness, for starters. Certainly there are people with mental illnesses who abuse drugs, and there are some drugs (e.g. cannabis) where extended heavy use can cause mental illness, but the two should never be considered synonymous.
Suicidal ideation certainly can be a symptom of mental illness, most obviously depression. However it can also arise from extreme sadness (which is not the same thing as depression), such as the death of a loved one. It can also be a reasoned response to other profoundly negative life events such as the loss of a job, chronic pain, homelessness or severe bullying, which the person cannot see a way through. Whilst there is more of a link than with drug abuse, you still need to be very careful about making that link.
If these links do exist for someone, they will be linked to some identifiable condition. In that case, the most important feature of this mental illness from the point of view of someone employing you is that your condition should be managed appropriately, most likely with medication. At that point they shouldn't need to consider it. You may need to include it in any medical statements, and your follow-up appointments may be covered in the same way as for any other employee with a medical condition. But this isn't who you are now, because your medical condition is managed, and it no more counts as "diversity" than, say, a history of obesity solved with a gastric band.
Diversity is about who you are, not about what your history is. There certainly are conditions which would be appropriate for inclusion under "diversity". My fiancee has a very mild form of Tourette's syndrome for example, and occasional mild physical tics do not affect her ability to work. Similarly, people with some degree of autism may need to wear noise-cancelling headphones in an office to limit their stimulation. The point of diversity is that if this doesn't affect your work then other people are expected to normalise it, and other people learning that there are other kinds of normal is always good.
I would still be wary about the "unique perspective" angle though. The point of diversity is to normalise these differences. If you're treating them like a special sparkly unicorn, you aren't looking at this as if it's normal. Diversity checklists of "one black, one wheelchair, one autistic, one gay" are a tokenism exercise which does no-one any good. Diversity is always an opportunity for people to learn how to do better, and that's going to benefit your organisation, because your organisation consists of people. But the point is considering them as equals, not something different and "special".
The post keeps changing, but I'd like to add my take on the questions currently in it.
Could such a candidate bring a unique background that could be valuable to an organization?
Yes. Anyone's lived experience provides some value to their organization, and unique experiences not fully represented by others in the organization provide a diversity of perspectives which is generally valued even further. However, whether that value will be recognized or valued by a hiring committee is a separate question, the answer to which is "sometimes yes sometimes no".
Would a Diversity statement be an appropriate place to raise those issues?
The use of the word "issue" is a bit ambiguous here, so I will address what I think are the two most common interpretations.
If you mean issue as in problem, then I would look at the Workplace.SE post mentioned by @lcrmorin in the comment to the OP. In general, it seems counterproductive to preemptively bring up potentially negative aspects of your application early on in the hiring process. If you will need particular accommodations due to your disability, when to raise these in the interview process is a bit of an open question (there are lots of related posts about the two-body problem). While you should not be misleading in your application, and while discriminating on disability (such as mental illness) is illegal in the US, mental illness is still strongly stigmatized and it is impossible to control how people will react.
If you mean issue as in topic, then I think it would be suitable for a diversity statement. However, the goal of the diversity statement is not to learn what demographics groups you fall into so that the department can fill out their diversity bingo card. Rather, the main purpose of the statement (in my view) is to gauge how well you will be able to contribute to the organization's goals surrounding diversity/etc. These goals are often described on a department's website, and commonly include things like improving student outcomes (e.g. enrollment, graduation %, feeling of belonging, etc.) for those from underrepresented groups or providing a diversity of perspectives on research, department culture, etc. Who you are and your history (including current and past struggles with mental illness, substance abuse, self harm, etc,) are both potentially relevant for such a statement, if they make you a good candidate for contributing to the department's diversity goals.
As an explicit example: graduate students suffer from high rates of mental illness, so having faculty who are familiar with the impacts of mental health and can provide mentorship/guidance/support to these students is beneficial. Critically, however, being mentally ill does not automatically make you this person. Someone who is not mentally ill but has demonstrated a past history of passion regarding mental health advocacy would better suit the department's needs than someone who simply listed that they are mentally ill.