Can mental health facilities hire people who have mental disorders?

That would depend. On the illness and the compliance of the patient. So if a person has had one episode of major depression 5 years ago with no subsequent illness, why wouldn't they be able to work with other people who have similar porblems?
Yes in some cases. they are employed a peer support specialist, the theory is that those who had gone through the same issues can help those going through the same and offer support from someone who not only understand,, but has gone or is still living with their disorder or issues.