A while ago I lose most of my crew after sinking a lot of ships, not knowing why. Turns out when they're downed in combat, even though Berath's challenge doesn't apply, they get injured like party members (not ship combat injuries), and they get cured when consuming food and drink everyday. Thank god they don't need I do a rest. Because of how weak most of them are, fighting multiple ships in a short time can get them a lot of injuries and potentially killed.

Yes, and it is a good way to eliminate some crew members 😄
I think there's no reason to do it (you can park them in the specific slots in ship GUI) but if you wanna lost one of it definitely... well, you can!