Haha, I wrote that a sim can never go to a hospital unless they're in the doctor career but a pregnant sim can, of course, go to the hospital to give birth.
When it's time to auto-age, sims just leave work and go home. Normally, if a sim arrives late for work and leaves early (due to auto-age-up), their work performance bar takes a considerable hit (sliding to the left) at the end of the work shift.
I've never had a sim leave work early due to sickness, though, so I was wondering if being sent home due to sickness also caused the performance bar to move back.
I'll keep my eyes peeled and let us both know.