I wouldn't, but that's me. I had thought about applying for part-time work at one (once when hypomanic) but really don't think they'd consider me. I used "experience" at one in an inquiry and heard nothing back.

I think a lot of people with psych issues consider jobs in the psych field. I think they know that. That's not to say they wouldn't consider a former patient, but it would be something they might in hiring, whether for better or worse.

Two years is not a long time. I think many hiring managers would agree. Also know that hiring managers do often Google candidates. They may look you up in their system. Maybe.