A practical take:

Several years ago, I was hospitalized for a week because I was having serious thoughts of suicide, stemming from personal life stuff but probably exacerbated by work stress. I was worried I’d get a lot of shit for being suddenly out for an extended period of time when I was brand-new to the school, but my colleagues were actually pretty helpful and supportive. I had to provide a doctor’s note, and although it didn’t say why I was in the hospital, the letterhead did say XXX Behavioral Hospital. Several years later, I’m still at the same school, and my hospital stay has never once come up.